STRAIGHT OFF A DECEMBER red-eye from the Amazon, Alex Atala is back home, sitting at the buffed ipê wood bar of his São Paulo restaurant D.O.M.—rated the best on the continent and fourth best in the world—talking about the time he was kidnapped.

"In the Amazon," says Atala, who is 44 and freshly sunburned, with tightly cropped gray hair, countless tattoos and a graying red beard that resembles van Gogh's, "this kind of thing can happen." It was 1998, the year before D.O.M.'s inception, and Atala had embarked...