Preheat oven to 350°F.
Heat skillet to medium. Add 2 Tablespoons olive oil and heat through.
Carefully add chicken pieces to the oil. Cook for 7-8 minutes, stirring occasionally, until chicken is cooked through and no longer pink. Set aside.
In the meantime add cubed potatoes and butternut squash to a stock pot filled with water. Bring to a boil, cooking for approximately 8-10 minutes, or until tender.
Drain water from the stock pot. Combine chicken with potatoes and squash. Add 1 cup shredded cheese. Stir together. Salt and pepper to taste.
Add 1/4 cup filling to each tortilla, rolling up and tucking ends under. Place in a large casserole dish.
Continue to do this until all tortillas are filled and in the pan (the pan will be tightly full).
Pour enchilada sauce over the enchiladas. Top with remaining 1 cup of cheese.
Bake at 350°F for 20-25 minutes, or until cheese is melted.
Serve alone or top with shredded lettuce and tomatoes.