Combine chicken, tomatoes, onion, chilies and cumin in small mixing bowl. Mix well.
Combine sour cream, 3/4 cup cheddar cheese, Monterey Jack cheese, and egg.
Grease 2 quart oven safe casserole. Spread half the corn chips in dish.
Layer with half the chicken mixture and half the sour cream mixture. Repeat chicken and sour cream layers.
Top with remaining corn chips and 1/4 cup cheddar cheese.
Cook using INDIRECT METHOD (one side of the burner) at MEDIUM for 1 hour.