Cuando bailando con Maria, Carlos dice, bamboleate guapa, mientras pensando, chevere!
In terms of its origins, it derives from the African which means that with all due respect to the Venezuelans and Puerto Ricans that have already posted (I am Puerto Rican), the word was almost certainly popularized first in CUBA where Afro-Caribbean culture was strongest. For example, the word was already being used in very early rumba/mambo songs (e.g. Guaguanco Callejero) for as long as we have had recorded evidence. Cuba was the first major exporter of Afro-Caribbean culture to the Spanish-speaking world (and indeed to the entire world), so it was from Mambo songs played on the radio that the word probably disseminated into the popular culture.
The reason why the word may be associated with Puerto Rico more now is that since the 60's - after Cuba was cut off from the world - Puerto Rico became the main proponent of Afro-Caribbean culture (and has itself been surpassed in the last decade or two by the Dominican Republic). Sorry Venezuelans, but to my knowledge Venezuela has never been a major exporter of Afro-Caribbean culture to the rest of the world.
Que chevere que conseguiste un nuevo trabajo.
Estuvo muy chevere la fiesta.
I don't know about the origin, but it's common in Peru.
B: Que chevere!