Heat a gas grill to medium-high or prepare a charcoal grill for direct medium-hot grilling.
Put the chicken in a shallow baking dish and season liberally with salt and pepper (I use about 1 teaspoon kosher salt and 1/2 teaspoon pepper for 4 breasts). Add the herbs and garlic to the breasts and drizzle with olive oil, turning to coat them evenly.
When the grill is ready, cook the chicken until browned and cooked through, about 6 minutes per side.
Arrange the chicken on a platter. Spoon the tomato salad over the top and serve.
To make the topping, combine all ingredients in a medium bowl and toss gently. Taste for seasoning and add more salt or vinegar to taste.
Assemble the dish and keep at room temperature for 2 - 3 hours.
Drizzle the dish with balsamic vinegar to finish, if you like.
Serve with crusty toasted bread or over pasta
Shave Parmesan cheese over the top, or top with sliced mozzarella balls