In a medium, nonreactive bowl, combine the ketchup, honey, vinegar and garlic. Mix well, cover and refrigerate for at least 1 hour.
Preheat oven to 350 degrees F (175 degrees C).
Heat the olive oil in a large skillet over medium high heat. Add the chicken parts and saute for 2 to 3 minutes per side, just to sear the meat. Transfer chicken to a 9x13 baking dish and cover each piece well with the reserved sauce.
Bake at 350 degrees F (175 degrees C) for 35 to 45 minutes, basting with the sauce every 15 minutes.