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1.
A party or gathering in which guests are allowed to invite themselves over to someone's house or car in order to smoke weed, usually for free.
Hey man, I just got paid today. Do you want to buy an ounce of weed, call up some people, and have a Jamaican Barbeque?
by Gabriel Sa August 21, 2008
 
2.
When guests invite themselves over to smoke weed.
"Hey man, the door was unlocked, we let ourselves in, can we burn with you guys?"

"Man what is this? A "Jamaican Barbeque "?
by Gabriel Sa August 17, 2008