As chief of staff and counselor to Hillary Clinton at the State Department, Cheryl Mills worked ceaselessly to help a South Korean garment maker open a factory in Haiti, the centerpiece of United States government efforts to jump-start the island nation’s economy after the 2010 earthquake. Ms. Mills took the lead on smoothing the way for the company, Sae-A Trading, which secured millions of dollars in incentives to make its Haiti investment more attractive, despite criticism of its labor record elsewhere. When she presided over the project’s unveiling in September 2010, she introduced Sae-A’s chairman, Woong-ki Kim, as the most...