Preheat grill or grill pan to medium-high. Rub chicken with 1 tsp oil and sprinkle with a pinch each salt and pepper; grill 4 minutes per side or until cooked through.
Toss cut vegetables with remaining 2 tsp oil and a pinch each salt and pepper; grill 5 to 7 minutes per side until tender.
Slice chicken. Spread rolls with tapenade, and fill with chicken, vegetables, and basil, if desired.
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