Kellogg Brown & Root, the nation's top Iraq war contractor and until last year a subsidiary of Halliburton Corp., has avoided paying hundreds of millions of dollars in federal Medicare and Social Security taxes by hiring workers through shell companies based in [the Cayman Islands]. More than 21,000 people working for KBR in Iraq - including about 10,500 Americans - are listed as employees of two companies that exist in a computer file on the fourth floor of a building on a palm-studded boulevard here in the Caribbean. Neither company has an office or phone number in the Cayman Islands. The Defense Department has known since at least 2004 that KBR was avoiding taxes by declaring its American workers as employees of Cayman Islands shell companies. With an estimated $16 billion in contracts, KBR is by far the largest contractor in Iraq, with eight times the work of its nearest competitor. The no-bid contract it received in 2002 to rebuild Iraq's oil infrastructure and a multibillion-dollar contract to provide support services to troops have long drawn scrutiny because Vice President Dick Cheney was Halliburton's chief executive from 1995 until he joined the Republican ticket with President Bush in 2000. The largest of the Cayman Islands shell companies - called Service Employers International Inc., which is now listed as having more than 20,000 workers in Iraq, according to KBR - was created two years before Cheney became Halliburton's chief executive. But a second Cayman Islands company called Overseas Administrative Services, which now is listed as the employer of 1,020 mostly managerial workers in Iraq, was established two months after Cheney's appointment.