In large bowl, whisk together oil, lemon juice, vinegar, oregano, Italian seasoning, salt, pepper and garlic. Transfer 4 tsp (20 mL) of dressing to glass bowl; add chicken and turn to coat. (Make-ahead: Cover and refrigerate for 30 minutes or up to 1 day.)
To remaining dressing, add tomatoes, cucumber, yellow pepper, onion and olives; toss and set aside.
Place chicken on greased grill over medium heat (350°F/180°C). Grill, covered, for 6 to 8 minutes per side or until no longer pink inside and a thermometer inserted in thickest part of chicken registers 165°F (74°C). Divide chicken and salad among serving plates and sprinkle with cheese.