Preheat 2 T vegetable oil in skillet. Remove seeds from chilies. Chop chilies, then saute with minced garlic in oil. Drain and break up tomatoes. Reserve 1/2 cup liquid. Add tomatoes, 1 tsp salt, oregano and reserved tomato liquid. Simmer, uncovered until thick, about 30 minutes. Remove sauce from skillet and set aside.
Combine chicken with sour cream, cheese and remaining salt. Heat 1/3 cup oil.