In a large pot of boiling, salted water, cook the rice, uncovered and stirring occasionally, until tender, about 30 minutes; drain.
Meanwhile, in a large skillet, heat 2 tablespoons olive oil over medium heat. Add the onion and jalapeno and cook until the onion is browned, 7 minutes; transfer to a bowl.
Add the remaining 2 tablespoons olive oil to the same skillet and increase the heat to medium-high. Season the chicken with salt and pepper, then add to the pan and cook until browned, 5 to 7 minutes. Add the pineapple and jerk marinade and simmer until the chicken is cooked through, 2 to 3 minutes. Stir in the onion mixture, black beans and cilantro; cook until the beans are heated through, about 1 minute. Season with salt and pepper and serve over the rice.