Step 1Place the chicken breasts between 2 layers of plastic wrap. Using a kitchen mallet, lightly pound the chicken breasts, flattening to about 1/4 inch thick. Place the chicken in a glass dish and drizzle with the garlic oil, turning so all sides are coated. Cover and marinate 15 minutes.
Step 2Meanwhile, heat a grill to medium-high. Grill the chicken until browned on one side, about 5 minutes. Season with salt and pepper to taste, turn and grill until the other side is browned and the chicken reaches 165 degrees on a meat thermometer, another 3 to 5 minutes. Remove to a warm platter. Squeeze the lemon half over the chicken.
Step 3Toss together the basil, cilantro, oregano, onion, cucumber, olives and salt to taste. Spoon the cucumber mixture over the grilled chicken and serve.