Preheat oven to 350°F. Remove giblets from interior of the chicken and pat chicken dry with paper towels.
Quarter onion and carrots and place into the bottom of a 4-6 qt dutch oven.
In a small bowl combine butter, olive oil, rosemary, thyme, salt and pepper.
Rub the butter mixture all over the skin of the chicken.
Place the chicken breast-side up in the dutch oven and cover. Roast for 1 hour 30 minutes to 2 hours, until the thickest part of the thigh registers 165°F on a meat thermometer.
Remove the lid of the dutch oven for the last 15 minutes of cooking to allow the skin to crisp up.
Remove from oven and let rest for 10–15 minutes before carving. This keeps the juices locked in.