Put the chicken into a shallow dish. Grate the zest from the lemon over the chicken. Cut the lemon in half and squeeze over the juice. Add 3 tablespoons of the oil along with the thyme, and garlic. Mix everything together so the chicken is well coated with all the flavorings. Cover and let sit for 30 minutes, or refrigerate for up to 4 hours.
While the chicken is marinating, prepare the tomato salad: Cut the tomatoes into 1/2-inch pieces and put them into a bowl. Add the vinegar, and remaining 1 tablespoon olive oil. Season, to taste, with salt and pepper, tear in the basil leaves, and gently mix to combine.
When you are ready to cook, remove the chicken from the marinade, scrape off the herbs, and season with salt and pepper. Heat a large skillet over medium-high heat and put a thin coating of olive oil into it. Cook the chicken, working in batches if necessary, until it is golden brown and cooked through, about 3 to 4 minutes per side. Remove the chicken from the pan and let it rest for 5 minutes.
To serve, place 2 pieces of chicken onto a plate, and spoon 1/4 of the tomato salad over the chicken. Spoon on some of the tomato juices as well. Repeat with the remaining chicken and tomatoes and serve.
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