For marinade, in a small bowl whisk together oil, vinegar, thyme, salt, and crushed red pepper. Reserve 2 tablespoons of mixture; set aside.

Place chicken between two sheets of plastic wrap; pound lightly with the flat side of a meat mallet to about 1/2-inch thickness. Place in a resealable plastic bag set in a shallow dish. Add remaining marinade; seal bag. Marinate at room temperature about 15 minutes or in the refrigerator for up to 1 hour.

Lightly grease the rack of an indoor electric grill or lightly coat with nonstick cooking spray. Preheat grill. Drain chicken, discarding marinade. Place chicken on the grill rack. If using a covered grill, close the lid. Grill until chicken is no longer pink (170 degree s F). For a covered grill, allow 3 to 4 minutes. For an uncovered grill, allow 8 to 10 minutes, turning once halfway through grilling.

Brush cut sides of bread with reserved marinade. Place bread, cut sides down, on grill rack. If using a covered grill, close the lid. Grill until lightly toasted. For a covered grill, allow 1 to 2 minutes. For an uncovered grill, allow 2 to 4 minutes, turning once halfway through grilling. Remove bread from grill.

To serve, place a chicken breast on each grilled bread slice. Spread with cheese. Top each sandwich with sweet pepper and basil. Makes 4 sandwiches.