In a small bowl, combine the cherry tomatoes, sun-dried tomatoes, capers, garlic, red wine vinegar, 1 tsp of the thyme, 3 tbsp of the olive oil, 1/4 tsp salt and a few grinds of pepper. Set aside, stirring occasionally to let the flavors combine.
Preheat grill for high heat.
Put the chicken in a shallow pan. Rub the chicken all over with salt (about 1/2 tsp. for each piece of chicken), a few grinds of pepper, and the remaining 1 tsp thyme. Drizzle remaining olive oil over each side of each piece of chicken and rub all over.
Lightly oil the grill grate. Place chicken on hot grill and cook for 6 to 8 minutes on each side, or until juices run clear.
Transfer the chicken to serving plates and top each with a generous serving of tomato salsa.