Late at night in the privacy of his room, with his Remington 870 pump gun and his Fender Telecaster Custom guitar at the foot of his bed and his Eerdmans' "Handbook to the Bible" on the shelf next to "The Rolling Stones Complete," Randy Reed of Vienna, Va., dreams about the day he will become an Eagle Scout.

"It's a warm, swelling feeling," he says.

And his chest fills with pride, which is, of course, what being an Eagle Scout is all about.

Last June, Reed went on a church mission to Robbins, Tenn., to help rehabilitate shelters for the needy and complete his Eagle Project, as he must to join Scouting's elect. On the first day of the mission, he dove deep into Webb's Creek and rescued Ken Newsome, his friend, a mission leader, from certain, murky death. For this Reed received a kiss on the cheek and the Boy Scouts' highest medal of valor, the Honor Medal for Lifesaving with Crossed Palms, at a Court of Honor in the Vienna Presbyterian Church Wednesday night.

One day this spring, the Court of Honor will convene again and Randy Reed, senior patrol leader of Troop 152, will become an Eagle Scout. He has one more merit badge to complete before his 18th birthday in April.

This afternoon, Reed will put on his uniform and his Britches bomber jacket and go to the White House to have lunch with President Reagan to celebrate the 75th anniversary of the Boy Scouts.

Reagan is the ultimate Boy Scout -- honorary national chairman, though he never was a Scout as a boy. He has tapped into the virtues that Boy Scouts everywhere hold dear: God and Country. It is morning in America: the era of wholesome chic. Scouting is back. The Eagle soars.

Reagan has "typified those things you read about in the Boy Scout manual," says Sen. Lloyd Bentsen Jr. (D-Tex.), who can't remember what he did with his Eagle badge. "I guess I left it on my pajamas this morning."

A Boy Scout is Trustworthy, Loyal, Helpful, Friendly, Courteous, Kind, Obedient, Cheerful, Thrifty, Brave, Clean and Reverent, all the things Americans like to believe they are. And, further, Americans like to believe that if we are all those things we will climb the ladder of success, just as a Scout climbs from a Tenderfoot to a Star to a Life Scout. But not everyone reaches the pinnacle. Only 2.5 percent of all Scouts become Eagles. But anyone can. Anyone can become President. Isn't that the American Way?

Arthur Eldred, of Oceanside, N.Y., received the first Eagle in 1912. Alex Holsinger, of Normal, Ill., received the millionth Eagle in 1982.

The Eagle Scout is a reminder that there are still standards in this country. "He is an example to America," says Robert Gies, a 17-year-old Eagle from Owings Mills, Md., who spoke at the Pageant of Peace outside the White House last Christmas.

Neil Armstrong, the first man to walk on the moon, is an Eagle. Guion S. Bluford, the first black astronaut, is an Eagle. In the wake of Watergate, Gerald Ford was exactly what the country needed: an Eagle Scout.

The problem is that all this virtue invokes what some Scouts call the "goody-goody" issue.

"People think of Boy Scouts as the Goody Goodies of America, little Joe Scout, which they're not," Randy Reed says. "Send 'em out to Philmont (a Boy Scout wilderness camp) and then call the Boy Scouts wimps. I'd like to see some of those jocks go backpacking with 60 or 70 pounds on their back. I did it when I weighed 110."

Other Eagles: D.C. Mayor Marion Barry, heart transplant surgeon William C. DeVries, presidential Press Secretary James Brady, Sen. Bill Bradley (D-N.J.) and filmmaker Steven Spielberg, who first learned about photography in a Boy Scout class. "If I hadn't been a Scout, I'd probably have ended up as an ax murderer or a butcher in a Jewish deli," he said a couple of years ago.

More Eagles: retired general William Westmoreland, retired admiral Elmo R. Zumwalt, and 11 percent of the midshipmen at Annapolis. The National Eagle Scout Association, with 80,312 members and 272 chapters, is currently trying to locate the Oldest Living Eagle.

Eagles take this business seriously.

"Let me put it to you this way: I've never noticed them giving a merit badge for stand-up comedy," says Kevin Phillips, a management consultant for Touche Ross and Co., who got his Eagle in 1976.

Eagles Redux: Publisher Hedley Donovan; Mr. Cub, Ernie Banks; actor Ozzie Nelson; data systems tycoon H. Ross Perot; hotel magnate J. Willard Marriott Jr.; Pulitzer Prize winner Harrison Salisbury and Sen. Richard Lugar (R-Ind.).

Lugar knows exactly where his Eagle badge is: "At home in the upper drawer of my dresser," he says. "It's with the sash with the 21 badges in rows of three, down seven. I'm not sure that for a while certain Scouting virtues were in vogue. When I first ran for mayor of Indianapolis, I was characterized as a Boy Scout hardly dry behind the ears with the big city bosses sitting around waiting to devour someone like myself, a straight arrow, who did not have enough moxie, street savvy, to keep things afloat. Then Watergate came along. Everyone began to reevaluate. There was a preoccupation with ethics legislation and cleanliness of every facet of life and some of those street-smart types started to look like soiled merchandise."

In 1972, there were 1,949,000 members of the Boy Scouts, says Joseph Merton, national director of the Boy Scouts division. By 1979, enrollment fell to 1,055,000.

"At a conference at Kent State in 1979, the youngsters called us pigs," Merton says.

By Dec. 31, 1983, Boy Scout membership was up to 1,116,332, with overall membership, including Cub Scouts, Explorers and adult Scouts, up 2.5 percent, the fifth consecutive increase after more than a decade of decline.

For a while, the Boy Scouts strove for the fashionable '70s goal of "relevance." Camping was out, and no longer a required merit badge. Environmental sciences were added. Now camping is back on the merit badge list.

Eagles Addenda: Redskins quarterback Joe Theismann and television personality David Hartman just missed. They hold the rank of Life Scout.

Stephen Kilsheimer made it to Eagle last Sunday. He is 26 and has Down's syndrome. He could have elected to go for optional badges offered to the handicapped. He refused. "I did it the hard way," he says.

For his cooking badge, he made a meal for his family. "I fixed Hamburger Helper, noodles and meat."

He works 30 hours a week in a greenhouse and sings in the young-adult choir of the Association for Retarded Citizens. For his Eagle project, he stripped the floor of the church in Durham, N.C., where his troop meets. Last Sunday, in his family's church, with the mayor and congressman present, he received his Eagle.

"I was tickled," he says. "It was important to me. I was excited. I was really shook up about it especially since I am handicapped."

His mother, Colleen, listening in on an extension, says, "He's been hearing that word a lot recently. It's kind of coming into his awareness. We never talked about it very much."

Alex Holsinger, the millionth Eagle Scout, is blond, blue-eyed and red-cheeked. At 16, he has not yet shed the roundness of boyhood. Sitting uncomfortably in a hotel bar, sipping a Coke, he is asked what it means to be an Eagle.

"It really means to me that you're an adult," he says. "I hate the stereotype, by the way. A lot of people would despise you if you said, 'Oh, little old lady, let me help you cross the street.' "

So far, he has 67 merit badges, 46 more than are required to become an Eagle. He wants to get as many as he can before he turns 18. The only one he's sure he isn't interested in is rabbit raising, which he says is "weird." His uniform is blazoned with awards and patches and medals, testifying to his uncommon success, and he isn't even wearing them all.

He has come to Washington to receive the Boy Scout Youth Leadership in America Award. He is the third person in the country to get it.

He completed his Eagle in 24 months, two more than the minimum.

Then he received a visit from Bob Pomeroy, director of the National Eagle Scout Association, informing him he was the millionth Eagle.

"It was like going to Central Casting when we found him," Pomeroy says.

All the Scout honchos came to his Court of Honor.

"I had nothing to do with planning it," he says. "There were people actually asking me for my autograph."

He got a letter from former president Ford (the first of four), congratulating him and "saying how it really sorta rounded him out," Holsinger says.

He has appeared on "Good Morning America," "Today" and "CBS Morning News" and has given "a jillion interviews." He is a walking, talking advertisement for the American boy. He says he wants to be a minister when he grows up.

He is asked how it feels to be the Perfect Kid.

"Sometimes I feel I'm just a publicity stunt for the Boy Scouts, but I really believe I've gotten so much out of it, including a $3,000 scholarship," he says. "I've gotten so much knowledge and so many friends. If they're using my face, my title, more power to them."

Eleven aging Eagles, who make up the national committee of the National Eagle Scout Association, are sitting around a conference room in the Gateway Marriott, planning their participation in the National Jamboree this summer. They have come from all over the country, some in their adult Boy Scout uniforms (gray slacks, blue blazer, red, white and blue striped tie), living examples of the credo: Once an Eagle, Always an Eagle.

They hear a report on the progress of the Eagle video program being made available to help establish new chapters. They examine the red, white and blue buttons and red, white and blue Eagle Jamboree patches and take time out from their business, in voices heavy with emotion, to talk about what it means to be an Eagle.

"There is no typical Eagle," says Dr. Hal Yocum, an orthopedist from Golden, Colo. "They're tall, they're skinny, they may be nerds."

"Eagle Scouts are not different from other people," says Marshall Bryant of Basking Ridge, N.J. "We get hurt, we get disappointed. We are not an elite. Never, never use that word. We just got caught up in a progression and climbed to the top of the mountain."

Pomeroy, a full-time employe of the National Eagle Scout Association, told about his troubled youth and the day it caught up with him, when the juvenile court judge told him he had a choice between reform school and the Boy Scouts.

He survived a rugged first night under the stars when the other Scouts, disliking his attitude, crushed eggs all over his head. He stayed, thanks to the intervention of his Scoutmaster and the darkness of the night, and was accepted by the others in the morning. "It was the first time I felt I belonged," says Pomeroy.

Randy Reed answers the door of his parents' house in Vienna, Va., in a blue button-down shirt and a tie, with his Fender Telecaster under his arm. "Don't get the wrong idea," he says. "Usually I'd be in a tattered Stones T-shirt and jeans. I'm into diversity."

He is a junior at Oakton High School, as comfortable in the 9:30 club as he is in his Boy Scout uniform. He has been with other Scouts in uniform after meetings "and they wouldn't go into a grocery store and buy stuff," he says. "It makes me wonder how much it means to them."

Sometimes the experience comes in as handy as it did that day in June when he saved the life of a man who outweighed him by some 70 pounds. Be Prepared. Reed was. Part of his Eagle project was to be in charge of first aid for the mission. He reviewed his lifesaving course before they left.

It was a hot day and they wandered up the creek looking for a place to swim. They found the ledge with the steel cable dangling from a tree that the locals had told them about. Then Ken Newsome fell headfirst, hit a rock and sank into the water.

The water was dark, 15 feet deep, and murky. Reed was afraid the undertow would carry Newsome away. Finally, through the blackness, he saw a patch of green -- Newsome's bathing suit. His shoulder had wedged in a crevice at the bottom of the creek. Reed put his left hand over Newsome's mouth and nose. Together, they floated to the surface.

He doesn't remember much of that. He was running out of air. "I remember it getting brighter," he says. "The rest of me was so freaked out. I don't remember any pain at all. I just remember feeling incredibly powerful."

He forced the water out of Newsome's lungs and saw his friend recover consciousness. "He kissed me twice, on the cheek," Reed says.

The rescue didn't make the papers, except the church bulletin, until Newsome and Scoutmaster George Baker insisted that Reed apply for the Lifesaving Award. Only four were given in 1984. At the ceremony Wednesday night, the Scoutmaster read letters from the president, Virginia Gov. Charles Robb, Rep. Frank Wolf and Martha Pennino, vice chairman of the Fairfax County Board of Supervisors. Reed got a standing ovation and a $100 savings bond. "I knew it was going to be good," he says. "I heard 'Jumpin' Jack Flash' on the way over."

There was a pot-luck dinner with tuna casserole, lasagna, fried chicken and a cake decorated with the Honor Medal for Lifesaving without the crossed palms. Reed drank lemonade. He is allergic to milk, which is as un-American as he gets.