Possibly from one of Lew Lehr’s comedy shorts from the Thirties showing chimps and monkeys doing silly anthropomorphic things like that, all with the catchphrase “Monkeys is the cwaziest peoples!”.
This first aired on a David Letterman show in the mid-late 90s. I saw it the first time he did it and liked it so much that I wrote those words as lyrics for my song Bipedal Faster. Sorry I can’t find an esact date that it first aired.