Spray 3- to 4-quart slow cooker with cooking spray. In cooker, spread 1 can of the green chiles. In medium bowl, mix remaining can of green chiles, the soup, enchilada sauce and mayonnaise.
Arrange 1/3 of the tortilla strips over chiles in cooker. Top with 1 cup of the chicken, 1/2 cup of the beans, 1/2 cup of the cheese and 1 cup of the enchilada sauce mixture, spreading to edges of cooker to completely cover tortilla strips. Repeat layers twice, reserving last 1/2 cup of cheese.
Cover; cook on Low heat setting 6 to 7 hours.
Top with remaining 1/2 cup cheese. Cover; cook about 5 minutes longer or until cheese is melted. Serve with tomatoes, lettuce and sour cream.