Preheat oven to 350°F.
Pat chicken dry with paper towels inside and out. Season generously with salt and pepper, including inside the cavity.
Heat butter and olive oil in a large Dutch oven over medium-high heat. Once hot, brown chicken on all sides until golden, about 4-5 minutes per side. Remove chicken from pot and set aside.
Add carrots, celery, and onion to the pot. Cook until vegetables begin to soften, about 8-10 minutes.
Pour in wine and scrape up any browned bits from the bottom of the pot. Cook until the wine is reduced by half.
Add chicken broth, thyme sprigs, and bay leaves.
Return chicken to the pot, breast-side up. The liquid should come about halfway up the sides of the chicken.
Cover the pot and transfer it to the oven. Cook for 45 minutes.
Remove the lid and continue cooking for 15 minutes more, or until the chicken reaches 165°F in the thickest part of the thigh.
Let rest for 10 minutes before carving.