In Iceland! He was only 64 years-old:

Bobby Fischer, the first U.S.-born chess player to become world champion, died yesterday in Iceland of an unspecified illness, the FIDE World Chess Federation said. He was 64, and had lived in secrecy and obscurity for decades.
Born in Chicago and raised in New York, Fischer became the youngest U.S. national champion by age 14 and a grandmaster a year later. In 1972, he defeated Russian champion Boris Spassky in a world championship match in Iceland at the height of the Cold War. The game became known as the “match of the century” and his win was a monumental event in an era during which Soviet players dominated the game.
He was regarded as the greatest U.S. chess player. “The gap between Mr. Fischer and his contemporaries was the largest ever,” fellow grandmaster Garry Kasparov wrote in the Wall Street Journal in 2004.
Fischer was known for unpredictable tactics at the board, keeping opponents guessing by rarely repeating opening strategies during matches, and displaying a genius for attack. He often unnerved opponents with what some of them considered psychological warfare. For example, Fischer didn’t show up for the second game of the 1972 Spassky match, voluntarily conceding a point. Chess writers have speculated on how much such a move affected Spassky.
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In 1992, Fischer emerged for a re-match with Spassky in Yugoslavia. He won the match, taking some $3.5 million in prize money. The U.S. government issued a warrant for his arrest for taking part in the competition, claiming he violated United Nations sanctions against the country. By then, a split in chess authorities meant Kasparov was widely recognized as world champion, although Fischer objected.