Preheat oven to 400 degrees. Coast a 9x13 casserole dish with nonstick cooking spray.
In a medium-sized bowl, combine all dry cornbread ingredients. In a small bowl, whisk together wet ingredients and 1/3 cup of cheese. Add wet to dry and mix until just smooth, then fold in green chilis.
Pour cornbread mixture into prepared casserole dish. Bake until you can insert a toothpick and it comes out clean, about 15-20 minutes. Poke holes a few holes in the cornbread so the sauce can get in there a bit.
While the cornbread is cooking, bring all enchilada sauce ingredients (except for the chicken) to a boil in a sauce pan, then simmer. Continue to simmer until sauce has slightly thickened, about 10 minutes.
When sauce is done, toss with cooked chicken. Spread sauce/chicken mixture evenly over the cooked cornbread. Top with remaining 1 cup cheese. Return to oven and cook until sauce is bubbling and cheese has melted, about 20-25 minutes.