The competition, devised by digital agency Steel, asks songwriters to create a Greggs Christmas song and submit it on the baker's Facebook page.
Lyrics have to be written to the tune of a famous Christmas carol. The winning song will be made into an e-Christmas card and shared on the Facebook page.
Five entrants will also be selected to win one free Greggs lunch every week for a year.
Newcastle-based Greggs was founded in 1939 and has 1,450 stores in the UK.
In February this year, Greggs rolled out a £4m integrated campaign, created by Gratterpalm, including a TV ad featuring real Greggs employees.
Scott Jefferson, the baker's customer and marketing director, was recently poached by pet store chain Pets at Home, to become its new marketing director.