This happened back in the 80s.
You may remember a gentleman named David Letterman had a television show on NBC back then. it was called 'Late Night with David Letterman'.
I was watching one evening. And David said 'Ladies and Gentlemen, we have a very special guest tonight- Dr. Hunter S. Thompson.'
*mad applause* Out slunk a Dr. Thompson who looked coked to the gills and completely uncertain about the bright lights and the undivided attention of thousands of people he could see (and how many millions he couldn't?).
'Dr. Thompson! It's great to have you here!' Dave greeted him.
'There're CIA men in your green room.'
'...' said Dave.
'They were telling me how they killed JFK. And Marilyn. And they're gonna kill me, too. FUCK I need a cigarette.'
Now, someone backstage at Letterman made a grevious error in judgement. They allowed the good Doctor to carry a satchel onstage with him. Said satchel was about 6" wide, about 12" long, and maybe 2" thick. At this juncture the good doctor started digging through it. Presumably for the aforementioned cigarettes.
While ranting on and on about the CIA men in the green room, he excavated a small ziploc baggie of red M&Ms and waved it around in one hand. I assume that's what they were, because clearly nobody would let him on stage with upwards of 20 500mgmethamphetamine tabets -- EDIT: they were downers, as 
prickvixen pointed out below.
You can probably tell I wasn't much of a user of pharmaceutical-grade sedatives, huh.
But the red M&Ms were not what we were looking for, though, and the Doctor stuffed them back into the bag. "Fuck, Dave, there's conspiracy everywhere." Here, is this the cigarettes? No, no, this is a bag of baking soda. About 5 grams of baking soda, carefully measured out.
THERE. There are the Kools. Dr. Thompson shoves one into his mouth, tucks the pack back into his satchel, and goes to excavate a lighter. In the process of digging for the lighter he produces
a CHROME-PLATED .44 AUTOMATIC
and waves it around on the stage, dig dig dig, rant ramble mutter mutter mutter. There's the lighter, the gun goes back in the bag, and we cut to David's face.
If you've watched Letterman much, you've almost seen the expression he was wearing.
Almost.
You know how there're moments where David is 'staring at something astonishedly' in a sketch? and you can tell it's fake shock- that he's going to grin at you any minute with genuine amusement?
This was the genuine 'OH MY GOD WHAT THE FUCK HAVE I DONE I AM GOING TO GET FIRED ANY SECOND NOW' moment. The moment I realized that no, that was not a bag of red M&Ms and a bag of baking soda. The moment I knew that the gun was real. And Dave turns to the camera and says, with a smile as stiff and saccharine as a wedding-cake decoration, "We're going to go to a commercial, we'll be right back!"
Commercial.
Back.
No Dr. Thompson.
No MENTION of Dr. Thompson.
No mention that there had Ever been Anything Named Dr. Hunter S. Thompson at Any Point in Recorded History.
...
I am not sure I ever laughed so hard in my life, before or since.
You may remember a gentleman named David Letterman had a television show on NBC back then. it was called 'Late Night with David Letterman'.
I was watching one evening. And David said 'Ladies and Gentlemen, we have a very special guest tonight- Dr. Hunter S. Thompson.'
*mad applause* Out slunk a Dr. Thompson who looked coked to the gills and completely uncertain about the bright lights and the undivided attention of thousands of people he could see (and how many millions he couldn't?).
'Dr. Thompson! It's great to have you here!' Dave greeted him.
'There're CIA men in your green room.'
'...' said Dave.
'They were telling me how they killed JFK. And Marilyn. And they're gonna kill me, too. FUCK I need a cigarette.'
Now, someone backstage at Letterman made a grevious error in judgement. They allowed the good Doctor to carry a satchel onstage with him. Said satchel was about 6" wide, about 12" long, and maybe 2" thick. At this juncture the good doctor started digging through it. Presumably for the aforementioned cigarettes.
While ranting on and on about the CIA men in the green room, he excavated a small ziploc baggie of red M&Ms and waved it around in one hand. I assume that's what they were, because clearly nobody would let him on stage with upwards of 20 500mg
prickvixen pointed out below. You can probably tell I wasn't much of a user of pharmaceutical-grade sedatives, huh.
But the red M&Ms were not what we were looking for, though, and the Doctor stuffed them back into the bag. "Fuck, Dave, there's conspiracy everywhere." Here, is this the cigarettes? No, no, this is a bag of baking soda. About 5 grams of baking soda, carefully measured out.
THERE. There are the Kools. Dr. Thompson shoves one into his mouth, tucks the pack back into his satchel, and goes to excavate a lighter. In the process of digging for the lighter he produces
a CHROME-PLATED .44 AUTOMATIC
and waves it around on the stage, dig dig dig, rant ramble mutter mutter mutter. There's the lighter, the gun goes back in the bag, and we cut to David's face.
If you've watched Letterman much, you've almost seen the expression he was wearing.
Almost.
You know how there're moments where David is 'staring at something astonishedly' in a sketch? and you can tell it's fake shock- that he's going to grin at you any minute with genuine amusement?
This was the genuine 'OH MY GOD WHAT THE FUCK HAVE I DONE I AM GOING TO GET FIRED ANY SECOND NOW' moment. The moment I realized that no, that was not a bag of red M&Ms and a bag of baking soda. The moment I knew that the gun was real. And Dave turns to the camera and says, with a smile as stiff and saccharine as a wedding-cake decoration, "We're going to go to a commercial, we'll be right back!"
Commercial.
Back.
No Dr. Thompson.
No MENTION of Dr. Thompson.
No mention that there had Ever been Anything Named Dr. Hunter S. Thompson at Any Point in Recorded History.
...
I am not sure I ever laughed so hard in my life, before or since.
he was not a fake, as some would say.
I'm guessing they offered to take the bag, but that never in a million years was he going to give it up. :)
Brilliant
Ha ha ha ha ha ha ha.
He'll be so missed.
Pev
Ahhh, thanks for the excellent retelling :)
Someone pointed out above that reds were dope, rather than speed, so that may explain a bit.
http://imdb.com/title/tt0083441/guests
Moreover, other apocryphal sources claim that he brought a live bomb on stage in 1983. (http://www.google.com/search?hl=en&lr=&q=hunter+thompson+david+letterman+bomb&btnG=Search)
Still, is there any credible record of his appearance? Other than your account?
This was the 4th hit at Google for 'Hunter S. Thompson Letterman'. the 3rd was gonzo.org.
So I'd suggest that yes, he appeared on Letterman in '85, as referenced at both links above. But hey, let's look for another appearance, why don't we?
Failed effort there, killjoy. ;)
HST
You still couldn't understand a word he said. (http://www.arguewithsigns.net/archives/2005/02/21/more_on_thompson_gonzo/)
Re: HST
Given that Shirley MacLaine tried to pull off his 'toupee' to his wailed protests and has been on since- and Crispin Glover kicked him in the head and came back again later, well. I think he's willing to bring back difficult guests.
And hey, I hadn't known that HST was a friend of Warren Zevon's, and wouldn't have if I hadn't gone digging. So if you're the anonymous party who kicked off the research, thanks. ;)