The performance is from the 1977 TV special "Bing Crosby's Merrie Olde Christmas." From Wikipedia:
Bowie's appearance has been described as a "surreal" event, undertaken at a time that he was "actively trying to normalise his career". He later admitted to having only appeared on the show because "I just knew my mother liked him". Buz Kohan was not sure that Crosby knew who Bowie was, but Ian Fraser claimed, "I'm pretty sure he did. Bing was no idiot. If he didn't, his kids sure did."
According to co-writer Ian Fraser, Bowie balked at singing "Little Drummer Boy": "I hate this song. Is there something else I could sing?", Fraser recalls Bowie telling him. Fraser, along with songwriter Larry Grossman and the special's scriptwriter, Buz Kohan, then wrote "Peace on Earth" as a counterpoint to "Little Drummer Boy". Crosby performed "Little Drummer Boy", while Bowie sang the new tune "Peace on Earth", which they reportedly performed after less than an hour of rehearsal.
A few days after the taping, Crosby said of Bowie, "clean-cut kid and a real fine asset to the show. He sings well, has a great voice and reads lines well."
