The Collaborative International Dictionary of English v.0.48:

Jamaica \Ja*mai"ca\, n.
   One of the West Indian islands.
   [1913 Webster]

   Jamaica ginger, a variety of ginger, called also white
      ginger, prepared in Jamaica from the best roots, which
      are deprived of their epidermis and dried separately.

   Jamaica pepper, allspice.

   Jamaica rose (Bot.), a West Indian melastomaceous shrub
      (Blakea trinervis), with showy pink flowers.
      [1913 Webster]