The Chicago Blackhawks were comfortable letting Hinostroza take all the time he needed to develop after selecting him in the sixth round (No. 169) of the 2012 NHL Draft.

After being drafted, the speedy forward played one additional season with Waterloo of the United States Hockey League, then started at the University of Notre Dame in 2013-14. Hinostroza had 32 points (eight goals, 24 assists) in 30 games and was named to the Hockey East All-Rookie team as a freshman.

In 2014-15 he led Notre Dame with 44 points (11 goals, 33 assists) in 42 games and was named to the Hockey East First All-Star team.

Hinostroza signed a three-year contract with the Blackhawks on March 21, 2015, and made his professional debut with Rockford of the American Hockey League on April 3, 2015.

He started the 2015-16 season with Rockford but was called up by the Blackhawks on Oct. 16, 2015, and made his NHL debut one night later, against the Columbus Blue Jackets. He played seven NHL games that season, and played for the United States at the 2016 IIHF World Championship.

Hinostroza started 2016-17 with the Blackhawks and scored his first NHL goal on Nov. 19, 2016, against the Vancouver Canucks, and had his first two-goal game against the Colorado Avalanche on Jan. 17, 2017.

He split 2017-18 between the Blackhawks and Rockford, playing 50 NHL games, including a three-point game against the Vegas Golden Knights on Jan. 5, 2018.