The Limousine Client is an older African-American gentleman who appears (understandably) to feel he is not getting value for money, since he hired Chance to protect him from the goons now confronting them. When Chance proceeds to extol the virtues of living life in the moment and expensive Japanese whisky, the Client reaches the very reasonable, and rapid, conclusion that Chance is not playing with a full deck. When he finally understands that his bodyguard is about to turn $900 worth of alcohol into a Molotov cocktail using a handkerchief and the car's cigarette lighter, he decides, apparently, that he's too old for this.
The character is played (far too briefly) by Danny Glover.
Given the portrayer of the role, this vignette is clearly designed to establish Chance as the spiritual successor to Martin Riggs.