Alice's first appearance on 'The Tonight Show' was on November 24th 1975 with guest host McLean Stevenson (who played Colonel Blake in M.A.S.H.).
He's second appearance on the show, with Johnny Carson, is the famous one. He appeared to publicise the then current 'Lace And Whiskey' LP. He performed the title cut in '40's gangster gear and tommy gun, with the giant chickens from the stage show.
On July 31st 1997, Alice appeared on 'The Tonight Show' again, this time with Jay Leno. He performed 'I'm Eighteen', and this was the first public appearance of Alice playing a guitar. He was not interviewed this time as the producers seemed to think that a woman with an iguana was more worthy of the air time!
There was a lot of discussion about why Alice did 'I'm Eighteen' on the Tonight Show that year. Just for the record:
On March 18th 2011 he was back on the show again, this time performing 'School's Out' with Dweezil Zappa on guitar, who happened to be sitting in with the house band that night, as well as a group of random backing singers in Alice make up. Alice appeared in full costume and make up and cane.
Then on September 9th 2011 he was back again, this time to introduce new guitarist Orianthi by playing 'I'll Bit Your Face Off' with the touring band from the 'Welcome 2 My Nightmare' album.