Combine the rosemary and wine in a saucepan. Bring to a simmer; remove from the heat and let it steep until cooled.

Lightly season the chicken with salt and pepper.

Melt the butter with the olive oil in a skillet over medium heat. Add the chicken pieces and cook until browned, turning to brown all sides. Add the wine and rosemary and cover the pan. Simmer the chicken for 25 minutes. Add the sliced mushrooms and continue cooking for 10 to 20 minutes.

Remove the chicken to a plate and skim the fat from the liquids. Spoon the defatted sauce over the chicken.