1. Put the tomatoes in a colander set over a bowl. Add 1/4 teaspoon of salt, toss well and let stand for 15 minutes to release the juices. Remove the tomatoes and whisk half the goat cheese into the tomato juices until smooth. Whisk in 2 tablespoons of the oil and season with pepper. Fold the tomatoes and the remaining goat cheese into the dressing.
2. Light a grill or heat a grill pan. Brush the chicken with the remaining 1 tablespoon of oil and season with salt and pepper. Grill over a hot fire or high heat, until golden on the bottom and almost cooked through, about 5 minutes. Turn the chicken and grill for 2 minutes longer, or until cooked through. Transfer to dinner plates, spoon the tomato and goat cheese salad on top and serve.
Notes: Grape tomatoes are small, oblong tomatoes with a very high sugar content. If they're unavailable, cherry tomatoes can be substituted but will add much less sweetness to the final dish.