Ivanka Trump and Jared Kushner are renting a Washington, D.C., home from a Chilean billionaire who bought it after the November election and whose company is embroiled in a dispute with the U.S. government over a mine potentially worth billions of dollars.

The six-bedroom house in the capital’s Kalorama neighborhood was bought for $5.5 million in late December by a company controlled by Andrónico Luksic, according to public records and interviews. Mr. Luksic’s family is the wealthiest in Chile, by some accounts, and controls...