Preheat the oven to 375°F (190°C). Spread about 1/2 cup of the green enchilada sauce evenly over the bottom of a 9x13-inch baking dish.
In a large bowl, combine the shredded rotisserie chicken, diced green chiles (with their juices), ground cumin, garlic powder, salt, and onion powder; stir until the chicken is evenly coated.
To assemble each enchilada, place some of the chicken mixture down the center of a corn tortilla, add about 1 tablespoon of sour cream, and sprinkle with shredded cheese (divide 1 1/2 cups of the cheese among the tortillas). Roll up the tortilla and place it seam-side down in the prepared dish.
Repeat with the remaining tortillas and filling until all are assembled in the baking dish.
Pour the remaining enchilada sauce evenly over the rolled tortillas so they are fully covered, then sprinkle the remaining 1 1/2 cups of cheese on top.
Bake uncovered for 25 minutes, or until the cheese is melted, the sauce is bubbly, and the center is heated through.
Remove from the oven and let the enchiladas rest for 5 minutes before serving.