Place chicken breasts between two sheets of plastic and pound until 1⁄4 inch thick. Season cutlets with 1 1⁄2 teaspoons salt and then lightly dredge with flour, shaking off any excess.
Place a sauté pan large enough to hold two cutlets in the oven; heat for 5 minutes. Add 1 tablespoon oil and then heat for 30 seconds more. Place the chicken cutlets in the pan in a single layer. Turn the chicken when it is lightly browned, about 4 minutes. Cook for about 4 minutes more. Remove to a plate, cover, and set aside in a warm place. Cook the remaining chicken, adding more oil to the pan if necessary. In the now empty sauté pan, add the shallots, garlic, and tomatoes. Cook for about 3 minutes, or until the tomatoes begin to burst. Add the wine and capers and cook for 2 minutes more. Stir in the basil and cream. To serve, place chicken on a serving platter and pour the sauce over the top.