How to Make It
Place each chicken breast between 2 layers of plastic and pound to a 1/2-inch thickness. Transfer to a large plate. Cover the chicken and refrigerate.
Melt the butter in a medium skillet. Add the onion and cook over moderately low heat, stirring, until softened and browned, about 20 minutes. Add a few tablespoons of water to the skillet to keep the onion from sticking. Transfer to a small bowl and add the olives, rosemary and a pinch each of salt and pepper. Let cool completely.
Lay the chicken, skin side down, on a work surface and season with salt and pepper. Spread one-quarter of the filling on each breast, leaving a 1-inch border all around. Separate the skin from the meat. Roll up the meat; wrap the skin around the meat to enclose it. Tie each roll in 3 places with cotton kitchen string.
Preheat the oven to 375°. Heat the oil in a large skillet until shimmering. Season the chicken with salt and cook over moderately high heat until browned all over, about 10 minutes. Transfer the chicken to a rimmed baking sheet and bake for about 10 minutes, or until an instant-read thermometer inserted in the center reaches 135°. Let the chicken rest for 5 minutes, then discard the string. Slice the chicken diagonally 1/2 inch thick.
Meanwhile, set the large skillet over high heat. Add the shallots and cook for 1 minute, scraping up any browned bits. Add the tomatoes and any accumulated chicken juices and cook, stirring, just until heated through, about 4 minutes. Spoon the tomatoes onto individual plates and arrange the chicken on top.