Drain sun-dried tomatoes in a sieve over a bowl, reserving oil. Set aside 1 1/2 tablespoons reserved oil to cook chicken. Finely chop 1/4 cup tomatoes; set aside for sauce. Place remaining oil and tomatoes in sun-dried tomato jar; reserve for another use.
Place each chicken breast half between 2 sheets of heavy-duty plastic wrap; pound to 1/2-inch thickness using a meat mallet or rolling pin. Sprinkle chicken evenly with 1/8 teaspoon salt and pepper.
Heat 1 1/2 tablespoons reserved oil in a large nonstick skillet over medium heat. Add chicken; cook 6 minutes on each side or until done. Remove chicken from pan; keep warm.
Add chopped sun-dried tomatoes, 1/8 teaspoon salt, broth, oregano, and vinegar; bring to a boil, scraping pan to loosen browned bits. Cook until broth mixture is reduced to 1/2 cup (about 3 minutes). Serve sauce over chicken.