Preheat a large nonstick skillet over medium-high heat and season the chicken with salt and pepper. Add olive oil to the skillet and sear the chicken breasts, cooking for about 3 to 5 minutes on each side (depending on thickness) or until firm to the touch. Remove from the skillet and set aside.
Add the shallot and garlic to the skillet and cook for 2 minutes. Add the balsamic vinegar and simmer until it has almost disappeared. Immediately add the tomatoes and toss well. Cook until the tomatoes soften slightly, just a minute or two. Toss in the basil or parsley and season to taste with salt and pepper.
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