Not sure what's with all the weird replies for such a simple question.
Anyway, the best place is definitely The Chippy at The Gate. They use beef tallow to fry, so you get the authentic chippy experience. No where else in Chiang Mai does that (to my knowledge).
You can also try U.N. Irish Pub & Restaurant, they do decent fish & chips too. And O.M.G. Bar and Restaurant is quite good (their pizzas are nice as well).
One other place would be Archers Restaurant & Bar, but The Chippy at The Gate is definitely the best in my opinion.
Hope that helps