Put olive oil in a medium frying pan over medium heat. Add in mushrooms, garlic, thyme, basil, pepper, oregano and onion. Cook till onions and mushrooms are softened. Set aside to cool to room temperature.
Once mushrooms are cooled mix into cream cheese in a medium bowl. Stir in mozzarella until fully combined.
Line a 9 x 9" casserole dish with tin foil. Make a slice into the chicken till about an inch away from the end to make a pocket. Spoon cream cheese mixture into the chicken breast. Brush extra olive oil onto the top of the chicken breasts.
Bake in the oven to 30-35 minutes till chicken has been cooked through.