In a shallow 2-quart glass casserole, combine lemon juice, garlic, oregano, sugar and salt for marinade. Place chicken breasts in marinade, cover tightly and refrigerate 2 to 4 hours, turning occasionally.
Heat coals in grill to medium hot and grill chicken about 4 inches from heat for 5 to 7 minutes on each side. Do not overcook!
You can also microwave the breasts covered on HIGH for 8-10 minutes on each side.