I am not sure why, but chicken is associated with Christmas in Japan, probably just good marketing. MOS Burger has a cute Christmas offering of 5 partially deboned pieces of chicken (I think these are a combination of leg and thigh with just a little bone left for getting good grip). Packs of five can be had for 1,200 yen, but a discount is available for pre-orders. Also, you can buy coupons to give as presents.
The name for the promotion is Merry Xmos, cute..
Photo is a web capture for explanatory purposes, copyright belongs to the company.