In a medium sized bowl, mix together the mayonnaise, olive oil, lime zest and juice, chilli, cinnamon, allspice, coriander and thyme.
Then add the chicken breasts, season and coat evenly and then leave to marinade in the fridge for a couple of hours.
Preheat a griddle pan or barbecue. Peel and cut the pineapple into quarters, remove the core and cut each quarter in half. Season with pepper.
Place the chicken on the griddle or barbecue and cook for 20 minutes or until cooked, turning over every now and then. Cut into a thick portion and check that it is cooked through, with no pink showing. Once cooked remove and leave in a warm place.
Now cook the pineapple for 4-5 minutes on each side, or until the pineapple starts to caramelise and serve with a sprinkling of chilli.
See more Caribbean recipes
If you're barbecuing for lots of people, cook the meat in the oven first then finish it on the barbecue for flavour and to ensure that it is thoroughly cooked. This is particularly important for poultry.
For top tips on protecting you and your family when preparing raw meat and poultry, visit Food Safety in the Home and view the full Food safety at home video.