Several hours before serving or the day before (if time allows), rub the chicken pieces pieces with the garlic and place them in a deep china or earthenware bowl.
Combine lemon juice, olive oil, salt and pepper to taste, and oregano and pour over chicken.
Cover the bowl and refrigerate the chicken for 1 hour, turning chicken pieces occasionally.
When ready to cook, preheat the broiler to its highest setting. Remove chicken from marinade; discard marinade.
Combine the melted butter, 1/3 cup lemon juice, and remaining oregano to make basting mixture.
Arrange the chicken pieces on the broiler rack and baste with a little of the melted butter mixture. Reserve part of the basting mixture to serve over the chicken when served.
Broil the chicken 3-4 inches from the heat for 5 to 8 minutes per side, basting often.
Chicken is done when juices run clear when pierced with a sharp knife.
Remove to serving platter, pour reserved basting mixture over the chicken breasts and serve immediately.
This is also good done on a BBQ.