This appears to be one of those domes that they place around highly sensitive radar dishes. I never heard of it before I saw it. Some folks in a local bar say its been around for about 3 years and it seems to have been fully completed about a year ago. They also say its guarded by U.S. soldiers. Hmmm....
In reality it could be just a weather radar. Its location at one of the highest points in central Jamaica would be ideal for that. If you have a good imagination you could probably come up with some more exciting explanations. Notice that its diameter is much larger than the small houses below it.

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Pictures taken: Summer 1997
pdsalmon@cs.wisc.edu