Preheat the oven to 350°F (175°C) and move the rack to the top third of the oven.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the hot skillet and cook about 3–4 minutes per side, until mostly cooked through; reduce heat if the oil splatters. Transfer the chicken to a plate.
To the skillet, add 1/3 cup pineapple juice, juice of 1/2 lime, 2 heaping tablespoons tomato paste, 1 minced garlic clove, and 1/2 tablespoon jerk seasoning; stir to combine.
Shred the cooked chicken with two forks, return it to the skillet, and toss to coat in the sauce; cook 2–3 minutes to heat through and meld flavors.
Arrange a layer of tortilla chips on a baking sheet (about half the bag). Top with half the chicken mixture, some drained pineapple pieces, and half the cheese.
Repeat with a second layer of chips, the remaining chicken, more pineapple, and the remaining cheese; top with sliced jalapeño if using.
Bake the nachos 10–15 minutes, until the cheese is melted and the nachos are heated through to your liking.
While the nachos bake, prepare the toppings: slice the avocado, chop red onion, cut extra lime wedges, and finely chop cilantro.
Remove the nachos from the oven and top with avocado slices, chopped red onion, dollops of sour cream, cilantro, and extra lime wedges; serve immediately.