Preheat the oven to 350 degrees F (175 degrees C).
Place chicken breasts in the bottom of a casserole dish. Season with salt and pepper.
Combine Mexican-style tomatoes, rice, celery soup, and chicken soup in a bowl. Pour mixture over the chicken breasts. Cover casserole with aluminum foil.
Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 1 1/2 hours. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Remove aluminum foil. Add Mexican cheese blend and tortilla chips to casserole. Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Broil until cheese is melted and bubbly, about 5 minutes.