Bring the broth, vinegar, garlic, peppercorns, and bay leaf, to a boil in a small saucepan. Reduce the heat and simmer until the liquid is reduced to about 3/4 cup and the garlic is very tender, 8–9 minutes. Discard the peppercorns and bay leaf; puree the garlic mixture in a blender.
Sprinkle the chicken with the salt and pepper. Heat the oil in a medium nonstick skillet over medium heat. Add chicken and cook until browned, about 5 minutes on each side. Add the garlic mixture and capers; partially cover and cook, turning the chicken, until heated through, 2–3 minutes longer.
Meanwhile, mix the butter and flour in a small custard cup to form a paste. Stir it into the sauce until blended and smooth. Simmer until the sauce is thickened, about 1 minute. Yields 1 chicken breast half and 1/3 cup sauce per serving.