Do not skin or bone the chicken breasts. Sprinkle the chicken pieces with salt and pepper. Heat the butter in a skillet and add the chicken pieces, skin side down. Brown about 5 minutes and turn.
Scatter the onion and garlic between the chicken pieces and add the mushrooms and bay leaf. Cook about 5 minutes. Add the wine and cook until it is almost all evaporated.
Add the rice and broth, taking care that the rice does not rest on top of the chicken pieces. Cover closely and cook about 20 minutes or until rice is tender.