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 salt and pepper.
Heat 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.
Melt butter in pan over medium-low heat. Add garlic; cook 1 minute (do not brown). Add broth; bring to a boil, scraping pan to loosen browned bits. Cook until broth mixture is reduced to 1/2 cup (about 4 minutes). Remove from heat; stir in lime juice. Serve sauce over chicken; sprinkle with cilantro. Serve with lime wedges.