According to the Online Etymology Dictionary, this sort of usage of the letter Chi first showed up in "The Anglo-Saxon Chronicle" (whatever that was) as Xres mæsse around 1100 A.D., and later appeared as X'temmas (1551 A.D.).
Bartleby has this to say:
Xmas has been used for hundreds of years in religious writing, where the X represents a Greek chi, the first letter of Χριστος, "Christ." In this use it is parallel to other forms like Xtian, "Christian." But people unaware of the Greek origin of this X often mistakenly interpret Xmas as an informal shortening pronounced. Many therefore frown upon the term Xmas because it seems to them a commercial convenience that omits Christ from Christmas.
