Combine 2 tablespoons oil, vinegar, thyme and garlic; mix well. Brush over both sides of chicken and pepper.
Grill on a covered grill 5 to 6 minutes per side or until peppers are tender and chicken is cooked through.
Brush remaining 1 tablespoon olive oil over cut sides of rolls; place cut sides down on grill during last minute of grilling. Place arugula over bottom of rolls; top with chicken and cheese. Cut peppers into strips; arrange over cheese and close sandwiches with roll tops.