Technically yes, but Masterchief always seems to fight either solo or with very little aid. It's his speciality.
Well, if you let Cheif have Sgt. Johnson (Halo 2-style) then there is no dought about the Cheif being able to win.
But he doesn't this isn't Master Chief and friends vs. Predator, this is Master Chief vs. Predator. As in a one on one fight. Even then, that fight is barely fair, Chief still needs a couple of cannon fodder marines and a choppa to get to. I also took the liberty of spell checking your statement in the quote.
Chef:Today we are going to cook a a special delicacy called face hugger. Predator: Tilts his head and looks at him*
Thanks for the spell check, not too good with typing. But anyway, I was making a pun as to how Johnson was basically unkillable in the said varient of the series. Which brings back good memories of me abusing that benefit for entertainment purposes. And I know that this is supposed to be a one-on-one fight but we have in my view come to the conclusion that the predator would easily win the fight.