Preheat oven to 400˚F. Butter 2-quart baking dish. Bring large pot of water to boil. Cook pasta according to package directions just until al dente. Drain well. Set aside.
Meanwhile, heat oil in large skillet over medium-high heat. Add chicken, cumin, paprika and cayenne to skillet and cook, stirring occasionally, until chicken is just cooked through and no longer pink. Season with salt and pepper to taste. Remove chicken to large bowl. Set aside.
In same skillet, melt butter. Add sliced peppers and onion to pan and sauté until tender, about 5 minutes. Mix in garlic and green chiles. Sauté about 2 minutes. Remove from heat and transfer vegetable mixture to bowl with chicken. Add sour cream, shredded cheeses and pasta to vegetable and chicken bowl. Mix everything together until well combined. Transfer to prepared baking dish.
Bake 15 minutes, or until slightly browned and bubbling. Let cool briefly before serving.