By James Bamford On a heavily protected military base some 15 miles south of Washington, D.C., sits the massive headquarters of a spy agency few know exists. Even Barack Obama, five months into his presidency, seemed not to have recognized its name. While shaking hands at a Five Guys hamburger restaurant in Washington in May 2009, he asked a customer seated at a table about his job. “What do you [do]?” the president inquired. “I work at NGA, National Geospatial-Intelligence Agency,” the man answered. Obama appeared dumbfounded. “So, explain to me exactly what this National Geospatial…” he said, unable to finish the name. Eight years after that videotape aired, the NGA remains by far the most shadowy member of the Big Five spy agencies, which include the CIA and the National Security Agency. Despite its lack of name recognition, the NGA’s headquarters is the third-largest building in the Washington metropolitan area, bigger than the CIA headquarters and the U.S. Capitol. Completed in 20...