Place chicken in an 11- to 12-inch frying pan. Add mango nectar, broth, lime juice, ginger, and cinnamon. Cover and bring to a boil over high heat. Reduce heat and simmer until meat is no longer pink in center of thickest part (cut to test), 15 to 20 minutes total. Transfer chicken to a platter and keep warm.
Boil pan juices over high heat, uncovered, until reduced to 1 cup, about 5 minutes. Mix cornstarch with 3 tablespoons water, pour into sauce, and stir until boiling. Pour over chicken. Add salt to taste.