Cohiba is a brand for two kind of premium cigar. One is produced in Cuba for Habanos S.A, the Cuban state-owned tobacco company, and the other produced in the Dominican Republic. The name Cohiba derives from "Taino" words for Tobacco. The Cuban brand filled with tobacco which, unique to Cohiba has undergone an extra fermentation process.
Cohiba was established in 1968 as a limited production private brand supplied exclusively to Fidel Castro and high level officials in Communist Party of Cuba and Cuban Government. Often given as diplomatic gifts, the Cohiba brand gradually developed as a "cult" status. It was first released commercially for sale to the public in 1982.
The Cohiba brand name was registered in the United States by the General Cigar Company in 1978 and cigars using that trademark have been produced for the American market in the Dominican Republic on a large scale from 1997. This second incarnation is unrelated to the Cuban product of the same name. Most smokers in the US think they are smoking a Cuban cigar and the General Cigar Cohiba passes hands as if it is contraband. General Cigar Company does nothing to dispel this mistaken notion as that was the intention of appropriating the brand name.
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* All information and picture from Wikipedia.