The Washington Post explains:
The notion of pairing the resolutely white-bread Crosby with the exquisitely offbeat Bowie apparently was the brainchild of the TV special's producers, Gary Smith and Dwight Hemion, according to Ian Fraser, who co-wrote (with Larry Grossman) the song's music and arranged it.
Crosby was in Great Britain on a concert tour, and the theme of the TV special was Christmas in England. Bowie was one of several British guest stars (the model Twiggy and "Oliver!" star Ron Moody also appeared). Booking Bowie made logistical sense, since the special was taped near his home in London, at the Elstree Studios. As perhaps an added inducement, the producers agreed to air the arty video of Bowie's then-current single, "Heroes" (Crosby introduced it)
The original plan had been for Bowie and Crosby to sing just "Little Drummer Boy." But "David came in and said: 'I hate this song. Is there something else I could sing?' " Fraser said. "We didn't know quite what to do."
Fraser, Kohan and Grossman left the set and found a piano in the studios' basement. In about 75 minutes, they wrote "Peace on Earth," an original tune, and worked out an arrangement that weaved together the two songs. Bowie and Crosby nailed the performance with less than an hour of rehearsal.
And that was almost that. "We never expected to hear about it again," Kohan said. (click for more)
(From Boing Boing)