Combine 2 tablespoons olive oil, 2 tablespoons jerk seasoning, 3/4 teaspoon kosher salt, and the juice of 1 lime in a large bowl. Add 2 boneless skinless chicken breasts and toss to coat. Marinate for at least 30 minutes but up to 24 hours.
Heat a 10 or 12 inch skillet (preferably cast iron) over medium-high heat. Sear chicken for 3 to 4 minutes on the first side, until you get a nice crust. Flip the chicken, cut the heat down to low and cover 10 to 12 minutes, until an internal thermometer registers 160°F (it will continue cooking off the heat to reach 165°F). Transfer the chicken to a cutting board.
Add 1 bag of cabbage to the skillet and toss to coat in those chicken juices. If needed, add a bit of oil if there’s not any fat left in the pan. Cook for 3 to 4 minutes, tossing frequently until wilted. Stir in 2 tablespoons vinegar and 1 tablespoon butter. Season with 1/2 teaspoon kosher salt and keep stirring until tender and delicious. Adjust seasoning to taste - you might want more salt or vinegar.
Make the pineapple salsa by tossing 1 cup diced pineapple, 1 diced avocado, 1/4 cup finely chopped cilantro, the remaining 1 tablespoon olive oil, and the remaining juice of 1 lime in a bowl. Season to taste with salt.
Slice the chicken on the bias and serve over cabbage with salsa on top.