Tucked away on the Cayman Islands sits Ugland House, an unassuming, nondescript building of modest scale and size. However, according to a recent report by the Government Accountability Office (GAO), this five-story office building is home to more than 18,000 corporate entities, nearly half of which have U.S. ties.

In the past few years, the number of corporations flocking to places like the Cayman Islands to evade U.S. taxes has exploded. One of these companies, former Halliburton subsidiary KBR, has used offshore tax havens...