Heat the oil in a large, deep skillet over medium heat. Sprinkle salt over both sides of each piece of chicken; cook the chicken in the hot oil until browned on both sides, but still slightly pink in the center, 3 to 5 minutes per side. Remove chicken to a plate and set aside. Add the onion, garlic, and jalapeno pepper to the remaining oil in the skillet; cook and stir until the onion is tender and beginning to brown, 5 to 7 minutes. Stir the cherry and mango into the mixture; cook and stir until the liquid in the pan is slightly thickened, 3 to 5 minutes. Add the cherry juice, lemon juice, and brown sugar to the mixture; stir and return to a simmer.Advertisement
Return the chicken to the pan. Ladle some of the sauce over the chicken to cover. Return the mixture to a simmer and cook until the liquid thickens and the chicken is no longer pink in the center and the juices run clear, about 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Don't reduce the liquid too much-you'll want enough for serving over the chicken and also rice, if you choose it as a side dish.