Federer, who is seeking a record sixth Indian Wells title, extended his win streak to 16 straight matches, matching the start he had to the 2006 ATP calendar season.
In the semi-finals, Federer will face Croatian Borna Coric who outlasted seventh seeded Kevin Anderson 2-6, 6-4, 7-6 (7/3).
Federer won 70 percent of his first serve points, had just one double fault and broke Chung's serve four times in the one hour, 23 minute main stadium match.
He clinched the victory on the second match point when he blasted his 12th and final ace of the contest.
And this victory guarantees he will hold onto the top spot after Indian Wells.
This was the first match between Federer and Chung since the semi-finals of the Aussie Open when the Swiss was leading 6-1, 5-2 and Chung was forced to retire with a foot blister.
The bespectacled Chung, appearing in his fifth quarter-final in six tournaments this year, dropped to 15-6 on the season.
He's set to surpass Japan's Kei Nishikori as the top Asian player in the ATP rankings.
Federer said he plans to get ready for Coric the same way he prepared for Chung.
"He plays similar to Chung," Federer said. "A great mover and has got a world of confidence.
"I got to play aggressive tennis as much as I can. Pretty simple, not always easy to do."