Chop the artichoke hearts. Add hearts, chiles and cheeses to a bowl. Mix in the mayonnaise until well blended.
Add the mixture to an 8 x 12 (oblong) glass baking dish.
Cover with foil and bake in a 375 degrees F oven for 30 minutes. Remove foil after 30 minutes and bake for an additional 30 minutes uncovered. When top is a light to medium brown and bubbling, remove from oven. Serve with round Tostitos corn chips or whatever brand pleases you.