1. Cut chicken into 5 pieces. Place in a large pan, sprinkle with chili powder and cover with 1/2 cup water. Bring just to a boil, reduce heat to medium-low and simmer for 10 minutes, until a thermometer inserted in thickest part registers 165°F. Transfer chicken to a cutting board (pour out any remaining water), shred or cut into small chunks and return to pan.
2. Add beans, corn and salsa. Cook over medium-high heat, stirring, until mixture is hot, about 5 minutes. Remove from heat.
3. Preheat oven to 375ºF; mist a 9-by-13-inch baking pan with cooking spray. Lay a tortilla out on a work surface; spread 1/2 cup of chicken mixture down center. Roll up and place seam-side down in pan. Repeat with remaining tortillas and chicken mixture. (If you have chicken left over, spread it on top of enchiladas.) Bake for 10 minutes. Sprinkle cheese evenly over enchiladas; bake until cheese has melted and enchiladas are hot, about 5 minutes longer. Serve immediately.