In a 10-inch sauté pan (preferably not nonstick) boil down the broth until it is reduced by about 2/3. Pour it into a container and set aside. Rinse and dry the skillet.
Lightly film the pan with oil. Heat it over high heat. Slip the chicken breasts into the pan, sprinkling them with salt and pepper. Lightly brown them on both sides. Lower the heat to medium low, and cook uncovered, 4 minutes per side, or until they are firm but not springy when pressed. Remove the chicken to a serving platter and keep it warm.
Make the pan sauce by adding the garlic and vinegar to the pan. Boil, scraping up the brown bits in the pan, until the vinegar is boiled down to 1/4 of its original quantity. Stir in the reserved broth and boil for 2 minutes, or until the sauce is rich tasting (it need not be thick). Adjust the salt and pepper. Stir in the butter until it's barely melted, and immediately pour the sauce over the chicken, topping it with the almonds.