Preheat oven to 400°F and position rack in the center.
Combine the broth and wine in a 5½-quart Dutch oven. Rub the chicken with olive oil, season inside and out with salt and pepper and place rosemary sprigs into the cavity. Truss the chicken with twine and place in preheated oven. Cook uncovered for 30 minutes.
Remove from the oven and nestle potatoes and carrots around the chicken. Season vegetables with salt and pepper and return pot to the oven. Continue to cook uncovered until an instant-read thermometer inserted into the thigh registers 165°F, about 60 minutes more.
Transfer chicken to a carving board, tent lightly with foil and let rest 10 minutes. Carve chicken and transfer to a warmed serving platter, serve with vegetables and pan juices.
