All great stand-up is the expression of a personal voice, no matter if it’s from a confessional, observational or prop comic. Mr. Chappelle has never been an exhibitionist onstage but his new material, even when oblique, seems revealing.

His stories wander but their baggy structure provides a nice frame on which to hang jokes. Part of the pleasing unpredictability of his delivery is that Mr. Chappelle would rather seem to stumble into punch lines than be guided by them.

In that same “Actors Studio” interview, the host, James Lipton, who has become friends with Mr. Chappelle, says that Richard Pryor’s wife felt that legendary comic had “passed the torch” to Mr. Chappelle. Like so many comics, Mr. Chappelle owes a debt to Pryor, and his career has in many ways retraced his steps. Both worked clubs in the Village and received big breaks from Mel Brooks (Pryor was a writer on “Blazing Saddles”; Mr. Chappelle appeared in “Robin Hood: Men in Tights”) before moving on to their own sketch shows and soul-searching trips to Africa.

Pryor cemented his reputation among many as the greatest stand-up of all time with the 1982 special “Live on the Sunset Strip,” only a few years after he accidentally set himself on fire while freebasing cocaine. He transformed a near-death experience into transcendent art. Mr. Chappelle has different demons and is a more elusive storyteller. What he burned up was not his body, but his career. Pryor located comedy in tragedy, but Mr. Chappelle deftly finds it in mystery.