I have looked at a track list for the album "A Little Christmas Music" by The King's Singers, and the only track with the word "gift" in the title is SIMPLE GIFTS.

Lyrics are posted here: Lyr Add: SIMPLE GIFTS (Joseph Brackett, Jr.), but I don't know whether the King's Singers sing all 3 verses.

(I don't think I'll e-mail Mario since the request is 11 years old.)