Through imported food, I would suspect that some GMO food can be purchased in the stores. But the local produce is pretty much organic as the trade has been passed down from generation to generation. The most recent info I can find is a march against Monsanto and GMOs.
http://iriefm.net/jamaicans-march-against-gmo-food/
I would look for Ital restaurants which serve organic food. Zimbali also has a Foodie Tour that can be found in Dining section.
I hope this helps a bit.
