Bring a medium pot of salted water to a boil. Add rice and cook over medium heat until rice is tender but still firm, 12 to 15 minutes. Drain in a sieve and rinse under cold water to separate grains. Drain well and set aside.
Whisk together lime juice, 2 tablespoons oil, molasses, garlic and jalapeno in a large bowl. Season with salt and pepper. Add beans, scallions, red peppers, 4 tablespoons of the cilantro and the cooked rice. Set aside.
Meanwhile, prepare the grill or preheat the broiler and broiler pan. Brush chicken with the remaining 1 teaspoon oil and grill or broil, basting with Pickapeppa sauce, until the meat is no longer pink in the center, about 4 minutes per side. Let cool slightly.
Cut the chicken in half lengthwise and cut into thin slices against the grain. Add to the rice mixture. Taste and adjust seasonings with salt and pepper. Garnish with lime wedges and the remaining 2 tablespoons cilantro.
Make Ahead Tip: Cover and refrigerate up to 1 day.