In a small bowl, stir the jerk seasoning and olive oil together into a thin paste. Rub evenly over both sides of the chicken breasts.
Grill or saute chicken for 4-6 minutes on each side, or just until it hits 165 degrees F and is no longer pink in the middle. Remove and set aside to rest briefly.
While chicken cooks and rests, prep the salsa. Combine avocado, red pepper, jalapeno, mango, red onion, cilantro, salt, and lime juice in a medium bowl. Toss gently to mix.
Serve individual chicken breasts with generous spoonfuls of salsa. Garnish with extra cilantro and lime wedges, if desired.