In a small saucepan, saute garlic in oil for 3-4 minutes or until tender; remove from the heat. In a 4-cup measure, combine the vinegar, ketchup, Worcestershire sauce, sugar, basil and garlic.
Pour 1 cup marinade into a large resealable plastic bag; add the meat. Seal bag and turn to coat; refrigerate for at least 6 hours or overnight. Cover and refrigerate remaining marinade.
Drain and discard marinade. Prepare grill for indirect heat, using a drip pan. Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack.
Grill steak, uncovered, over medium heat until browned on each side. Move steak to indirect side of grill, using a drip pan and grill, covered, for 45-50 minutes on each side or until meat reaches desired doneness (for medium-rare, a meat thermometer should read 145°; medium, 160°; well-done, 170°), basting occasionally with marinade. Yield: 6-8 servings.