Preheat the oven to 400°F/205°C.
Dry the chicken with paper towels. Season inside and outside with salt and pepper. Stuff the breast cavity with the garlic, onion pieces and thyme. Tie the chicken legs together with kitchen twine.
In an 8-qt. Dutch oven, heat the oil and butter over medium heat. Place the chicken in the pan and cook, turning frequently, until brown on all sides. Remove chicken from the pan and reserve.
Drain off all but 2 Tbsp. of the fat and return the pan to the burner.
Add the potatoes, onions, carrots and bay leaves. Position the chicken on top of the vegetables.
Pour in the chicken stock and wine and bring to a simmer. Season the dish generously with salt and pepper. Cover the Dutch oven and position it on the middle rack of the oven.
Cook for 30 minutes. Remove the cover and cook an additional 15 - 20 minutes or until the chicken juices run clear when the thigh is pierced with a knife.
Remove the chicken from the pan to a carving board. Stir the sugar snap peas into the pan and let them steep for 3 - 5 minutes.
Carve the chicken and arrange the pieces on a serving platter. Place the vegetables and pan juices in a bowl and serve alongside the chicken.