Between two pieces of plastic wrap, pound chicken to 1/2 inch thickness. Place in self-sealing plastic bag set in shallow dish. Add marinade; seal bag. Refrigerate 1 to 2 hours.
Drain chicken; discard marinade. In a large skillet cook onions and sweet peppers, covered, in hot oil over medium-low heat 13 to 15 minutes or until tender; stir occasionally. Uncover; add 2 cloves minced garlic; cook and stir over medium-high heat 3 to 5 minutes more or until onions are golden. Stir in vinegar and 1/4 teaspoon each salt and ground black pepper. Cook until vinegar evaporates. Remove from heat; set aside.
Grill chicken on rack of uncovered grill directly over medium coals for 8 to 11 minutes or until no longer pink; turn once. Combine butter and 1 clove minced garlic. Spread on cut sides of rolls. Grill rolls, cut sides down, 1 to 2 minutes until golden. Place cheese on bottom halves of rolls. Top with chicken and vegetables. Add tops. Makes 4 sandwiches.
Combine lemon juice, olive oil, Greek or Italian seasoning, salt, and black pepper.