Add oil to a large saute pan and heat over medium-high heat. Add the garlic and cook for 1 minute. Add the chicken and cook about 4 minutes per side, or until cooked through and juices run clear. Remove the chicken and set aside. Lower heat to medium and add the balsamic vinegar and chicken broth to the pan. Stir, scraping the bottom of the pan to remove any browned bits. Add the tomatoes, bring to a simmer and cook 3 to 5 minutes. Serve over chicken.