On a gloriously gusty day that stirred this gritty city's huge soul, the Chicago Bears routed the Los Angeles Rams, 24-0, to win the championship of the National Football League's National Conference, redeeming mournful years of failure by almost every Chicago team in almost every major professional sport.

As 63,522 fans deliriously chanted off the last five seconds today, the city erupted in a pandemonium of auto horns, shrieks, bellows, and telephone calls in a raw outpouring of delight and triumph unmatched since the Bears last won an NFL championship in 1963.

Since then, Chicago's teams have come to the brink of national glory several times, only to lose ignominiously. For a city of sports fanatics a long, dark nightmare has ended.

With hopes for a Super Bowl victory two weeks from now soaring sky-high, Chicago tonight became a metropolis at last transported by the sweet, sweet sensation of victory. And so, too, is Boston, after the New England Patriots beat the Miami Dolphins, 31-14, in the American Conference championship game, ending a streak of 18 losses in Miami dating back to the 1966 season.

The Bears will now play the Patriots in Super Bowl XX on Jan. 26 at 5 p.m. in New Orleans.

"Am I happy? Is the pope a Pole?" said Jack Ewald, a Bears season-ticket holder who has attended every home game except one since 1954. Reflecting on the endless misery, Ewald asked himself again: "Am I happy? Is the pope a Catholic?"

The day was typically Windy City: it dawned with a piercing blue sky and blustery winds sweeping out of the northwest, that made the bare trees bob and groan. The buffeting increased, "blowing every which way," as Bears quarterback Jim McMahon said after the game.

By kickoff, the temperature hovered near freezing and the wind was whipping at 25 mph over Soldier Field, the colonnaded playground by Lake Michigan where the Bears have gone unbeaten this year. Papers, streamers, dust, magazines, and everything that wasn't nailed or glued down flew through the air around the stadium. Perfect Bears weather.

"This is the very best!" shouted Tony Terry, as the wind clawed at his words in the highest row of seats atop the stadium. "They're charged! They're firing!" Terry, an 18-year-old high school senior, said he is completely confident the team will win the Super Bowl.

If they play as they did today, they will be hard to beat.

From kickoff to final second, the Bears dominated. They bottled up the Rams' feared running back, Eric Dickerson, holding him to 46 yards rushing, and throttled the Rams' quarterback, Dieter Brock, holding him to 10 completions in 31 passes, only 66 yards in the air.

It was the first time in NFL history that a team has registered back-to-back shutouts in the playoffs. Last Sunday, the Bears eliminated the New York Giants, 21-0.

McMahon scored the Bears' first touchdown on their first possession, on a 16-yard run after a broken play. The extra point made it 7-0. Then Kevin Butler kicked a 34-yard field goal, and the Bears were in front, 10-0.

Scoring resumed on a long drive in the third period that ended with a 22-yard McMahon pass to Willie Gault, the Bears' fleet-footed wide receiver. In the fourth period, Chicago's fearsome defensive end, Richard Dent, sacked Brock, who fumbled the ball. Outside linebacker Wilber Marshall scooped up the free ball, shook off a near-tackle, and ran 52 yards for the final score.

The Bears head to their first Super Bowl with the best overall record, 17-1, since the Dolphins' undefeated season in 1972.

Kevin Collins, a 29-year-old food broker and native Chicagoan, said, "It's been such a long, long time coming. Hell, I can barely remember when they won in '63."

The Bears went into today's game the heavy favorites against Los Angeles, which brought a 12-5 record to Chicago. This morning, they were a 10 1/2-point favorite, but fan Mike Gierut, 16, noted with amazement that "The Greek Jimmy Snyder, the CBS handicapper picked L.A. If I coulda' found anyone to take my money, I'd have put a bundle on the Bears all the way."

As it was, he was waiting for the results of a $15 pool he shared with his father. But even if they lost the money, he didn't care. "It's great," he said, his face a huge smile swathed beneath a knit cap and tightly-tied parka hood.

The wind pouring over the city ushered in ranks of clouds that soon settled lower and lower along with the Rams' hopes. As the game wound down, the stadium was enveloped in swirling snow, the perfect metaphor for the cleansing this single football victory means to Chicago.

Twice before in the past three years, Chicago teams had carried the city's hopes to the brink of fulfillment -- and then dropped the ball. In 1983, the Chicago White Sox ended a 24-year long case of baseball miseries by winning the American League's Western Division title. But then they lost the pennant to the Baltimore Orioles.

In 1984, it was the National League Chicago Cubs' turn to raise, then dash, the city's hopes. The Cubs won the National League Eastern Division title, their first championship in 39 years, then lost the pennant to the San Diego Padres.

The Bears carried the city's hopes anew last year, when they reached the National Conference championship game, but lost to the San Francisco 49ers. The 49ers went on to beat Miami in the Super Bowl.

Ask anyone in the Windy City tonight, and they will tell you the Super Bowl winners this year will be . . . the Bears! Hope springs eternal, and at long last, it might be rewarded.