I'm going under the assumption that Chuck Norris WOULD have been a ninja if his beard didn't shred through the outfit. and that Chuck Norris does not blend.
Chuck Norris would win
Chuck Norris is a 68 year old Martial Artist who, in 1997, was the 3rd westerner to recieve the rank of 8th Degree Black Belt Grand Master in Tae Kwon Do. A ninja, in modern dialogue, is a practioner of the Ninjustu martial art no matter what level they are. So in view of this, Chuck Norris would usually win but he might not if the ninja was sufficiently well trained.
They would engage in fierce conbat, but theyd be so evenly matched, they would cause a rip in the fabric of existence and cause the universe to implode. and the only survivors would be the ninjas mask,
and Chuck Norris's Beard