Pound the chicken breasts between sheets of plastic wrap until they reach a uniform thickness of half an inch.
Season the flour with salt and black pepper in a shallow bowl.
Dredge each piece of chicken lightly in the flour, shaking off any excess.
Heat olive oil and one tablespoon of butter in a large skillet over medium-high heat.
Place chicken breasts into the pan and sear until golden brown and cooked through, about 3-4 minutes per side. Remove and set aside.
In the same pan, add the remaining butter and mushrooms, sautéing until caramelized.
Add the minced garlic and cook for 1 minute until fragrant.
Deglaze the pan with grape juice, balsamic vinegar, and chicken stock, scraping up any browned bits.
Simmer the sauce until reduced by half and slightly thickened.
Return the chicken to the pan to coat with the sauce, then garnish with fresh parsley and serve.