Cook chicken breasts by boiling or baking until fully cooked. Shred the chicken.
Heat olive oil in a skillet over medium heat. Add chopped onion and cook until softened, about 5 minutes. Add minced garlic and cook for 1 minute more until fragrant.
Stir in enchilada sauce, diced green chilies, chili powder, cumin, salt, and pepper. Bring to a simmer and cook for 5 minutes.
Add the shredded chicken to the sauce mixture and stir to combine.
Warm the corn tortillas slightly to make them pliable. You can do this by wrapping them in a damp paper towel and microwaving for 30 seconds, or briefly warming them in a dry skillet.
Spoon about 1/4 cup of the chicken mixture into the center of each tortilla. Sprinkle with 1 tablespoon of Monterey Jack cheese and 1 tablespoon of cheddar cheese.
Roll up the tortillas and place them seam-side down in a 9×13 inch baking dish.
Pour the remaining enchilada sauce over the rolled tortillas.
Sprinkle the remaining Monterey Jack and cheddar cheese evenly over the top.
Bake for 20-25 minutes, or until the cheese is melted and bubbly and the enchiladas are heated through.
Let stand for a few minutes before serving. Garnish with your favorite toppings if desired.
Notes
Warming the tortillas makes them easier to roll and prevents them from cracking.
You can adjust the spice level by using mild or hot enchilada sauce.
Feel free to add other vegetables like corn or black beans to the chicken mixture.