Chopra, 23, managed a winning best of 87.58 metres to go one better than India's previous best: two silver medals won in the 200m and now-defunct 200m hurdles at the 1900 Paris Games by British-Indian Norman Pritchard.
The Czech Republic filled out the podium at Tokyo's Olympic Stadium, Jakub Vadlejch taking silver with 86.67m and Vitezslav Vesely claiming bronze with 85.44m.