Cook the chicken under the broiler until meat is cook through and browned on both sides, about 20 minutes. Make sure the chicken reaches an internal temperature of at least 160ºF. When the chicken is done, slice diagonally into 1-inch strips.
In a large mixing bowl, combine the cooked rice, black beans, bell pepper and cucumber.
In a medium size saucepan, simmer the reserved marinade and pineapple juice mixture over medium heat. Stirring occasionally, cook until the sauce reduces slightly, about 5 minutes.
Plate the chicken on top of the rice and bean mixture. Drizzle warm sauce over top and serve immediately.