GENERAL LEVALLE, Argentina—Pilots often stare in disbelief when they make their first flight over this hamlet on the verdant pampa. There, on the monotonous plain below, is a giant guitar landscaped out of cypress and eucalyptus trees. It is more than two-thirds of a mile long.

Behind the great guitar of the pampa, and its 7,000-odd trees, is a love story that took a tragic turn.

The...