A few of the times Gollum showed up on David Letterman in the early 80's.
Brother Theodore: My momsie and my popsie both died years before I was born, and my sister and my uncle were identical twins, which is probably more than you can say for yourself!
Letterman: You got me there, that's for sure.
Brother Theodore: I have nowhere to go, and no one to go with me. I roll in the gutter alone, unshaven, with a coated tongue and a bloodshot eye, and I have no dollar for dope, I hallucinate on tap water. I find it hard to sit still in one spot, and impossible to sit in two spots.
Letterman: You ever do any water skiing?
Nick Cave should write a song out of Brother Theodore lines.
Just in case it isn't common knowledge, Brother Theodore was the voice of Gollum in the 1977 Rankin/Bass cartoon of The Hobbit.