In a large nonstick skillet, melt the butter in the oil over medium heat.
Sprinkle the chicken on both sides with salt and pepper and lightly dredge in flour, tapping off any excess.
Fry the fillets, without crowding, until lightly browned, about 3 minutes per side. Transfer to a warm platter and set aside.
Add the broth, grape juice, and vinegar to the skillet, increase the heat to high, and stir, scraping up any browned bits from the bottom.
Cook until the liquid has reduced by half, than stir in the vanilla and taste for seasoning.
Pour the sauce over the chicken and serve immediately.