1. Start a charcoal or wood fire or heat a gas grill or broiler. The fire should not be too hot, but the rack should be fairly close to the heat source, at a distance of 4 inches or less. If necessary, you can pound the chicken slices lightly between two pieces of waxed paper so that they are of uniform thickness.

2. Rub the chicken with 1 tablespoon olive oil. While the grill is heating, heat remaining 2 tablespoons olive oil in a medium-to-large skillet over medium heat. Add garlic and cook, stirring, until it colors lightly. Add capers, and cook for 15 seconds. Add tomatoes, and cook over medium-high heat until thick, about 10 minutes. Taste, and add salt and pepper to taste, then cook 1 minute more. Set aside, keeping warm.

3. Grill or broil the chicken very quickly; it should take no more than 3 to 4 minutes per side. Serve the chicken with the tomato sauce, garnished with minced fresh basil or parsley leaves.