Preheat the oven to 375 degrees F (190 degrees C).
Arrange chicken thighs in a roasting pan; season with salt and pepper. Scatter onion over and around chicken. Top chicken with basil, garlic, and rosemary. Pour chicken broth into the pan and evenly distribute carrots around the chicken. Cover the pan with aluminum foil.
Cook in the preheated oven until chicken is no longer pink at the bone and the juices run clear, about 1 hour. An instant-read thermometer inserted near the bone should read at least 165 degrees F (74 degrees C). Remove aluminum foil and continue cooking until chicken is browned, 10 to 15 more minutes.