The second main ingredient in JERK Chicken and other dishes is Allspice.  It is also called Jamaica pepper, kurundu, or myrtle pepper.  

It is a spice which is the dried unripe "berries" of Pimenta Dioica , a mid-canopy tree native to the Greater Antilles, southern Mexico and Central America, now cultivated in many warm parts of the world. 

The name “ Allspice" was coined as early as 1621 by the English, who thought it combined the flavor of cinnamon, nutmeg and cloves.  Allspice is one of the most important ingredients of Caribbean cuisine. It is used extensively in the Caribbean with jerk seasoning where the wood is used to "smoke" the Jerk Chicken in Jamaica.  

Allspice is also indispensable in Middle Eastern cuisine, particularly in the Levant, In Palestinian cuisine, for example, many main dishes call for allspice as the sole spice added for flavoring. 

In America, it is used and is also responsible for giving a unique flavor when used correctly on many dishes to create that Caribbean flavor.