Preheat oven to 400°F.

Place butter in a pan over medium heat. Add onion and garlic and cook until slightly softened. Add in mushrooms and cook until juices are released and reabsorbed. Add wine and thyme. Cook until evaporated but not dry. Cool completely.

Combine cooled mushrooms with cream cheese, mozzarella cheese and salt & pepper to taste.

Using a sharp knife, cut a 1 ½″ slit in the side of the chicken. Move the knife around creating a pocket. Fill the pocket with ¼ of the mushroom mixture. Repeat with remaining chicken breasts.