Preheat grill or cast iron grill pan to medium-high heat.
Remove any excess fat from chicken and rinse under cold water. Pat dry with paper towels. Use a pastry brush to brush with olive oil and season with 1 1/2 teaspoons jerk seasoning and salt, if desired. Set aside.
Drain pineapple slices and reserve juice. Season both sides of pineapple slices with 1/2 teaspoon of jerk seasoning; set aside.
In small saucepan, bring reserved pineapple juice, remaining 1/4 teaspoon jerk seasoning, and brown sugar to a boil over high heat. Reduce liquid by 1/2, about 5 minutes. Remove from heat and set aside.
Just before grilling, oil grate. Place chicken breasts on grate and grill for 4 to 5 minutes per side or until cooked through. Remove to platter and tent with foil.
Place pineapple slices on grate and grill for 1 to 2 minutes per side until grill marks appear and pineapple is heated through.
Serve chicken breasts with pineapple slices and warm sauce.
NOTE: Chicken may also be broiled 4 to 6 inches from heat source for 6 to 8 minutes per side. Broil pineapple 1 to 2 minutes per side.
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