Using a rolling pin, pound the chicken between 2 sheets of wax paper until they are of uniform thickness. Heat the oil and garlic in a large skillet over medium-high heat until the oil shimmers and the garlic browns. (Don't burn the garlic.) Add the chicken breasts and cook until golden, 3 to 5 minutes on each side. Add the salt, pepper, vinegar, chicken broth, and rosemary. Cover, reduce heat to medium-low, and cook 3 minutes longer or until the chicken is fork-tender. Remove the chicken to a platter and keep warm. Increase heat to high and boil the sauce until thickened or syrupy, 3 to 5 minutes. Whisk in the butter and pour the sauce over the chicken.