Pick the bocconcini out of the marinade. Transfer half of the marinade to a medium baking dish. Add the chicken, season with salt and pepper and let stand at room temperature for 1 hour or refrigerate for 4 hours.
Quarter the bocconcini and transfer to a bowl. Add the remaining marinade and the tomatoes and season with salt and pepper.
Light a grill or preheat a grill pan and oil the grate. Grill the chicken over high heat, turning once, until lightly charred and cooked through, about 8 minutes. Cut the chicken into bite-size pieces and add to the bocconcini. Toss and serve.