Which country is most famous for BBQ?

The Word 'barbecue' is from American (New World)-Spanish, 'barbecoa', originally from a Haitian Indian (Arawakan) term 'barbakoa', which described a raised frame of sticks.

These frames were used for various purposes, from drying clothes and leaves, to sleeping, and for holding meat over a fire, for smoking.

The term came to mean (a meal of) roast meat and by the nineteen-thirties was used in English to describe a grill used for cooking (usually meat) over a fire.