Cut tortillas into 1/2-inch-wide strips. Place strips in a single layer on an ungreased baking sheet, and coat strips with cooking spray. Bake at 350° for 10 minutes or until crisp. Let cool.
Combine chicken and 1/4 cup salsa in a large nonstick skillet. Bring to a boil over high heat. Reduce heat to medium-high, and cook 2 minutes, stirring occasionally. Remove from skillet. Set aside, and keep warm. Wipe skillet dry with paper towels.
Coat skillet with cooking spray; place over medium-high heat until hot. Add onion; saute 2 minutes. Add green chiles; saute 2 minutes. Add cheese and 1/4 cup sour cream; stir until cheese melts.
To serve, arrange tortilla strips evenly on individual serving plates. Top tortilla strips evenly with chicken mixture. Spoon onion mixture evenly over chicken mixture. Top each serving with 1 tablespoon of remaining salsa and 1 tablespoon of remaining sour cream.