Place the chicken breasts one at a time in between to pieces of parchment paper or plastic wrap and pound to a ¼-inch thickness. You can use a meat mallet or a rolling pin. The idea is to get the chicken to an even thickness all around. Set Aside.

Whisk together the lemon juice, olive oil, vinegar, garlic, parsley, oregano, salt and pepper in a glass baking dish.

Place the pounded chicken in the dish with the marinade and coat it thoroughly. Cover and marinate in the refrigerator for 4-6 hours or allow to sit at room temperature for 30 minutes if you’re in a hurry.

Heat the grill to medium.

In the meantime, prepare the vinaigrette: In a large skillet, heat 1 Tablespoon of olive oil and sauté the shallots until tender and translucent. Add the tomatoes and salt and sauté until they start to loose their shape, about 2-3 minutes, as your sautéing, try to mash the tomatoes slightly with your spoon. Turn off the heat and whisk in the Dijon mustard, remaining 2 Tablespoons olive oil and the vinegar. Stir in sliced basil. Set aside.

Remove chicken from marinade and place the chicken on the grill and flip when the edges of the breasts are white and they can be easily released from the grill. Continue cooking on the other side until the chicken reaches an internal temperature of 160 to 165 degrees. This should take around 4-5 minutes per side if you pounded the chicken breasts. Set chicken aside to rest, tented with aluminum foil.

Place the arugula on a large platter and place the chicken on top. Top with the tomato vinaigrette and serve.