Pat the chicken dry with paper towels and season it with ½ teaspoon salt and ¼ teaspoon black pepper.
Heat the butter and oil in a large skillet over medium high heat; once the skillet is hot, add half the chicken and cook until browned on both sides, about 4 minutes per side, flipping once. Transfer the browned chicken to a plate and cook the remaining chicken the same way.
Turn the heat up to high and add the wine; use a wooden spoon to scrape up any brown bits from the bottom of the pan. Add the garlic, remaining ½ teaspoon salt, and remaining ¼ teaspoon black pepper, and cook until the wine is reduced by about half, about 5 minutes, stirring occasionally.
Pour the sauce (including all the garlic cloves) into the bottom of a 9 x 13 inch casserole dish. Arrange the chicken on top and bake until the chicken is fully cooked, about 45 minutes.