Preheat oven to 400°F
Place butter in a pan over medium heat l. Add onion and garlic and cook until slightly softened
Add in mushrooms and cook until juices released and reabsorbed.
Add wine and thyme. Cook until evaporated but not dry. Cool completely
Combine cooled mushrooms with cream cheese, mozarella cheese and salt and pepper to taste
Rinse chicken breasts under cold water and pat dry with a paper towel. Using a sharp knife, cut 1 1/2 slit in the side of the chicken. Move the knife around creating a pocket. Fill the pocket with 1/4 of the mushroom mixture. Repeat with remaining chicken breasts
Place chicken breasts on a foil lined pan, sprinkle with salt and pepper to taste and bake 30-35 minutes (165°)