Preheat the oven to 200 degrees F. Season the chicken on both sides with salt and the jerk seasoning. Set aside while you cook the plantains.
Heat 2 tablespoons vegetable oil in a large nonstick skillet over medium-high heat. Add the plantains in a single layer and cook until golden brown, about 3 minutes per side. Transfer to a baking sheet and season with salt. Keep warm in the oven.
Add 1 tablespoon vegetable oil to the same skillet over medium heat. Add the chicken and cook until browned and cooked through, about 7 minutes per side. Transfer to a cutting board to rest.
Add the remaining 1 tablespoon vegetable oil to the skillet and increase the heat to medium high. Add the red onion, bell pepper, ginger, chile and a pinch of salt. Cook, stirring, until the vegetables just start softening, about 2 minutes. Add 1/2 cup water, the vinegar, pineapple preserves and 1/2 teaspoon salt. Bring to a boil, then reduce the heat and simmer 3 minutes. Discard the chile and stir in 1 tablespoon cilantro.
Slice the chicken and divide among plates along with the plantains. Spoon the vegetables over the chicken using a slotted spoon. Top with the remaining 1 tablespoon cilantro. Serve the pineapple sauce on the side.