The Cayman Islands were colonized from Jamaica by the British during the 18th and 19th centuries, and were administered by Jamaica after 1863. In 1959, the islands became a territory within the Federation of the West Indies, but when the Federation dissolved in 1962, the Cayman Islands chose to remain a British dependency.

https://www.cia.gov/library/publications/the-world-factbook/geos/cj.html

http://en.wikipedia.org/wiki/Cayman_Islands