Here's Chris (father of Abby) Elliott portraying "Marlon Brando" on David Letterman's old NBC show.
Elliott was a writer on the show, and Dave let him do bizarre (but funny) bits like this on a regular basis. (He still appears - less frequently - on Dave's CBS show).
Note: When Chris mentions "Foster Brooks" here, he's actually referencing Dave's interview with a seemingly drunk Oliver Reed.