Place chicken thigh in a ziplock bag and add buttermilk and salt and pepper. Marinate in refrigerator for at least 30 minutes. Remove, rinse and pat dry. Salt and pepper both sides.
Preheat oven to 450º. Butter a 13 x 9 inch casserole dish.
Cut acorn squash lengthwise and remove seeds. Cut each half crosswise into 1/2 inch slices. Place squash, carrots and onion into bottom of prepared pan.
Add chicken to top of vegetables, skin side down. Bake for 10 minutes. Remove from oven and turn chicken so that it is skin side up. Pour maple syrup over the top of the chicken and continue cooking for 25-30 minutes until a thermometer registers 170º and vegetables are tender. Skin should be golden brown.