As he picks his way along the jostling line, shaking a hand here, fielding a question there, always busily working the crowd, he has the happy air of someone entirely in his element. What would you expect from the man who is becoming the world's best-kn o wn defence lawyer?
This week the 57-year-old Mr Cochran, LA's top black attorney, will lead OJ Simpson's legal team in a televised courtroom battle which will be more widely watched than any other case in history. His shimmering suits, noisy ties and razor wit will soon befamiliar to millions of TV viewers around the world. He is the super-smooth king of LA's celebrity lawyers - and he is clearly loving the role.
A decade ago, there were only two or three internationally known names among the 70,000 lawyers working in and around LA. Howard Weitzman earned his golden spurs by securing an acquittal for John DeLorean, despite an FBI videotape showing his client sipping champagne in front of an open suitcase stuffed full of cocaine.
Marvin Mitchelson dominated the headlines for years with his exotic Hollywood "palimony" suits, before going down in flames when he was convicted of tax fraud. The rest grafted away in a city with a reputation as one of the toughest beats in the business. Some got rich. Others turned to haunting hospital corridors in the hope of finding litigation-minded patients.
But a combination of high-profile, sleaze-soaked cases and courtroom cameras has spawned a new generation of super-briefs - a handful of lawyers who are becoming almost as famous as their clients. Most come from California. Most have humble beginnings (Cochran is the grandson of a Louisiana sharecropper), but now move among Hollywood actors, producers, and society hostesses. And most are now millionaires.
Last year, the grand dame of LA lawyering was Leslie Abramson, the fiery New Yorker who became a media star as she sought to persuade a jury that Erik Menendez shot dead his rich parents because he had been abused as a child. The millions who watched herangrily shake her foaming blonde curls at the judge may not have agreed - but her style was gripping. Gripping enough to win her a $4,000-a-day contract as a TV commentator on the OJ case, plus a $500,000 book contract.
Cochran's appeal is different. A charismatic, fast-talking courtroom bamboozler, he won his reputation with cases against the police, repeatedly exposing misconduct, racism and brutality. He has won $43m in judgments, amassing a fortune which enabled himto buy his first Rolls-Royce in 1977. (It wasn't long before the cops saw him in it and, assuming it was stolen, stopped him at gunpoint).
Two years ago he entered the national spotlight by agreeing to represent Reginald Denny, the white trucker beaten up by black youths at the start of the LA riots. But he finally crossed the line into full-fledged stardom last year, when Elizabeth Taylor recommended him to her friend, Michael Jackson, in the midst of the entertainer's child sex abuse scandal. Cochran helped nail down Jackson's $32m out-of-court settlement with a 13-year-old boy.
His client list now includes the rapper Snoop Doggy Dogg, who is accused of participating in a drive-by murder. Almost everyone thinks he is the best lawyer that either Snoop or OJ can hope to find. But the prototype of the new LA celebrity lawyer is notso much Cochran as his colleague Robert Shapiro - who, until recently, headed OJ's defence, but agreed to play second fiddle after a row with F Lee Bailey, another prominent lawyer on the case. Ever since the bodies of Nicole Simpson and Ron Goldman were found stabbed to death outside an LA house last June, Shapiro has been the hottest property in town.
His tanned features seem to be everywhere. Not long ago, "Lunch with Shapiro" topped the bill at a silent auction during a Hollywood ball attended by, among others, Hillary Clinton, Warren Beatty, Arnold Schwarzenegger and the Duchess of York. He fetche d $2,000. A boxer (despite his 51 years), Shapiro posed with his gloves on for People magazine. Other pictures showed him lounging in bed and in the swimming-pool at his four-bedroom Beverly Hills spread. The New York Times has called him the "single most recognisable attorney on Earth." He has hired an agent to handle offers from book publishers.
Such unprecedented fame has given rise to fears among some lawyers that the line between the legal profession and the world of commercial entertainment has become blurred. A small tribe of lawyers are making a living as television "experts", commanding $2,000 a day. A witness in the trial and former friend of OJ, Kato Kaelin, has had a guest slot on a cable TV show. Even the judge, Lance Ito, has appeared in a five-segment interview with a local television station.
"All this is worrying, to the extent that there's a risk that lawyers will put their own interests before those of their clients," says Stephen Yagman, a civil rights lawyer in Los Angeles.
Only the prosecution lawyers have steered clear of the lure of fame - although they, too, have been unable to escape a peppering of stardust. Marcia Clark, the leading prosecutor, only earns a pittance (the going rate for her post at the Los Angeles District Attorney's office is around $100,000) compared to Mr Cochran and his silk-suited associates. But few doubt that the case has placed a high price on her head - and has guaranteed her a top job in private practice, if she wants one.
Like almost every aspect of the OJ case, her story reads like a script. She is a former dancer and was once married to a professional backgammon player, who was disabled after being shot in the head by his best friend.
Several months ago, the OJ prosecution team went to Arizona, where they summoned together a panel drawn from the public to see how they reacted to certain issues in the OJ case. Some grumbled about Clark's manner and appearance, saying she was too severe. She responded like the celebrity she has become: she went back to LA and had a make-over.