He recorded his only "hit," the song Paralyzed, in 1968, in apparently what was a moment of spare time in a recording studio in Texas. T-Bone Burnett played drums on the record. The lyrics to this magnum opus are unintelligible snarls, growls, and similar vocalisms, surrounded by frantic strumming on acoustic guitar, Burnett's equally frantic drumming, and occasional yelps of what sounds like the name of the song, "Paralyzed!"
500 copies of the single were the initial pressing. It earned the Cowboy an appearance on Laugh-In, the TV comedy show. Unfortunately, a musicians' strike forced the postponement of some follow-up TV appearances for Odam, and by the time the strike was over, his fifteen minutes of fame were up. Paralyzed went on to be featured on several Doctor Demento compilations, and it often appears prominently in lists of the worst recordings ever made. The Cowboy has recorded a number of novelty songs since Paralyzed, and one of them was in fact covered by David Bowie on his Heathens album. Odam returned the compliment by recording his version of A Space Oddity.