Place chicken thighs in a medium-sized bowl or marinating bag and drizzle with Jerk sauce; toss to coat. Set aside.
Preheat your grill on medium-high heat—about 400º F. (See notes for baking instructions.)
Prepare the pineapple, mango, red onion, tomatoes, cucumbers, cubed avocado, and parsley. Toss them all into a bowl together and set aside. If you simply slice the avocado, leave it aside to top the salads later. (I slice mine because I love big pieces of avocado in my salad, but this is a personal preference and it's delicious either way!)
Once the grill is heated, place saucy chicken breasts onto the grill and drizzle them with any leftover sauce they were sitting in. Grill for 5-7 minutes, flip, and grill for another 5-7 minutes or until they reach an internal temperature of 165º F and juices run clear.
While the chicken cooks, prepare the vinaigrette (recipe below).
Once the chicken is ready, slather them with some extra Jerk sauce and slice or cube them. Place mixed salad greens in serving bowls, top with fruit and veggie mixture, sliced avocado, and finally, top with the chicken. Drizzle with your desired amount of dressing and serve.