Heat a large skillet over medium high heat. Add oil to coat the pan. Season chicken pieces with salt and pepper. Add to hot oil, and brown for about 5 minutes. Remove from the pan, and set aside. Cover with foil to keep warm.
Add chicken stock, salsa verde, green chilies, half and half, and pasta to the skillet. Bring to a boil Cover and reduce heat to low. Cook for about 15 minutes, or until the pasta is cooked.
Add chicken back to the pan. Stir in 1 cup of cheese. Sprinkle remaining 1/2 cup over cheese over the top. Cover and cook for 2 minutes until melted.