The clash between the pair is a rematch of the Australian Open semi-final, which Federer was leading 6-1, 5-2 before Chung retired due to blisters on his foot.
Cuevas, world No. 34, couldn't do much to stop Chung in the first set, with the Korean securing an early lead 6-1.
The 27-year-old Raonic, who is ranked 38th in the ATP standings, made the finals of the BNP Paribas Open in 2016 before losing to Novak Djokovic. Federer can match his best start to a season if he overcomes Chung in the quarter-finals - he is now 15-0 in 2018, and can equal his 16-0 from 2006 when he was 24-years-old.
Federer qualified for the ATP Indian Wells Masters quarters on Wednesday. after he defeated Frenchman Jeremy Chardy in two straight sets 7-4 6-4.
Federer, who won the Australian Open in January, is gunning for a record sixth Indian Wells title.
Chung defeated Pablo Cuevas in straight sets, 6-1, 6-3, to reach the final eight at the BNP Paribas Open at Indian Wells Tennis Garden in Indian Wells, California, on Wednesday (local time). Federer has been clinical in his dismissal of three opponents without the loss of a set so far in his 2018 Indian Wells campaign.
America's Sam Querrey booked his quarter-final spot with a 6-3, 6-4 win over Spaniard Feliciano Lopez.
The 21-year-old Croatian, world No 49, started strongly but was pushed to a deciding third set only to recover from an early break deficit and clinch victory with his fifth break of the contest. With a new team, including coaches Riccardo Piatti and Kristijan Schneider, Coric has mounted somewhat of a resurgence at Indian Wells. He dropped just three points overall with those coming on his second serve. Chung has lost four of his last five quarterfinal matches.
"I'm just trying to (play) 100 percent my tennis, for sure, because he (plays) great tennis", Chung said of Federer, according to the Los Angeles Times.
The 20-year-old Russian needed just 58 minutes on Thursday to brush aside the German. In the day session, Angelique Kerber plays against Daria Kasatkina trying to continue her great season.
"I just fought and that's maybe why I won because I refuse to lose".
Martic controlled the second set, taking a 5-2 lead before Halep forced the tiebreaker.
Halep next plays the victor of a quarter-final between No. 5 seed Karolina Pliskova of the Czech Republic and Naomi Osaka of Japan.