Japan is holding controversial ex-world chess champion Bobby Fischer, wanted by the US for more than a decade.
Fischer, a recluse for years, was detained at Narita airport
Mr Fischer is accused by the US of breaking international sanctions by travelling to Yugoslavia in 1992 to play against a Russian arch-rival.
Mr Fischer, an American citizen, won the match against Boris Spassky but disappeared when the US authorities announced they wanted to prosecute him.
The 61-year-old says he will appeal against the extradition order.
The reclusive Mr Fischer, a fierce critic of America, was detained at Tokyo's Narita airport, apparently with an invalid passport.
Mr Fischer has managed to live undetected in Japan for three years, sometimes travelling abroad.
This time he was reportedly on his way to the Philippines.
A brilliant but highly mercurial player, Bobby Fischer became a grandmaster at 15 and shot to fame in 1972 when he beat Boris Spassky of the then-Soviet Union.
The match, played in Iceland, was billed as the "Match of the Century" and Mr Fischer's win was regarded as a propaganda victory as the game had been dominated by the Soviets since World War II.
He held the title of world chess champion until 1975 and then slipped in and out of the limelight, resurfacing in Yugoslavia for the dramatic 1992 rematch against Mr Spassky.
BBC correspondent Jonathan Head in Tokyo says Mr Fischer could face extradition to the US and a 10-year jail sentence.
Japan shares an extradition treaty with the US, obliging them to hand over anyone sought by America who enters or lives in the country.