Hot rumor at The Palm last night: Sen. Chris Dodd (D-Conn.) was bringing Bianca Jagger to the fifth anniversary celebration of Larry King's radio show.

He didn't.

"Oh gosh. I haven't seen Bianca in six or eight months," said Dodd, who arrived with a staff member. "But I always find this amusing. I guess it's a good selling point."

Dodd ducked out early and King seized the opportunity to announce, "I hope you'll understand Chris Dodd had to leave early because Bianca Jagger was waiting in the car."

In case you didn't know it, yesterday was Larry King Day in Washington. The mayor said so. President Reagan sent him a letter. The Palm, his favorite restaurant, closed its doors for his celebration. And 125 fans and former guests of the show gathered at Washington's clubbiest restaurant to fete King.

Even the waiters charmed the crowd by singing "Happy Anniversary" to King in front of a big cake with five candles.

The glib, Brooklyn-born radio talk-show host is known as a seasoned interviewer who never loses control of his guests or those hundreds of listeners nationwide who call in to his 12th-floor Crystal City studio in the middle of the night.

One wrong word and--Zap!--they're cut off.

But last night, live from The Palm, it was supposed to be a little different.

For the first time Larry King was to be at the mercy of some of those very same powers he has interviewed. But instead of the promised roast, everyone sang his praises. "He's a talent and he's unique," said Marty Rubenstein, president of Mutual Broadcasting Systems, which hosted the party and which airs King's show five nights a week. "We have a lot in common, we're good friends and we have a long contract so we don't have to worry about anything like that."

"We have a great communicator in the White House and we have a great communicator right here," said Bob Orben, the humorist and speechwriter.

The guest list was impressive: journalist Daniel Schorr, presidential aide Craig Fuller, former senator George McGovern, attorney Edward Bennett Williams and musicians Chuck Mangione and Peter Allen.

Williams, Mangione and Allen also were the guests on the midnight talk show, which aired from The Palm. Allen wore a blue golf cap. Mangione wore a black felt bolero-style hat. Neither took off his hatduring dinner.

King, a 25-year radio veteran, normally begins his Washington show at midnight. His format is: A guest takes calls from midnight to 3 a.m., at which time the guest leaves and the callers take over until 5:30 a.m. There never is a shortage of listeners volunteering their views.

Last night was no different. The program started right at midnight after a typical Palm he-man dinner: thick sirloin steaks, Palm fries and mountains of creamed spinach. A rather healthy slice of cheesecake came through for dessert.

Hot rumor No. 2: They were going to lock The Palm's doors at midnight so no one could leave until the show's end.

They didn't. But nobody budged--at least for a while.

After all, the first guest was Edward Bennett Williams, and there was no mystery about his subject: The NFL team he owns an interest in.

The Redskins, what else?