The name of the actor is a parody of Chuck Norris and Arnold Schwarzenegger.
Grand Theft Auto III
The actor appears to be a relatively high man and wears a blue suit. If the one looks closely, they can spot a beard, just like Chuck Norris has.
Grand Theft Auto: Vice City
The Vice City sighting of Chuck is on a billboard of the movie Half-Cocked, which is located around the City Model in InterGlobal Studios, Prawn Island. It is likely that textures were reused from Grand Theft Auto III.
Grand Theft Auto: San Andreas
If the one listens closely to some pedestrians, they can hear that the pedestrian saw Schwartz and his Half-Cock jogging near his house in Vinewood. This is actually a reference to the film he starred in.