The 36-year-old legend won his 20 grand slam title by winning Australian Open in January this year. In the victory, Chung won 73 percent of his first serve points and 54 percent of his second serve points.
That allowed Federer to repeatedly put Chardy under some pressure, although it took until the 11th game for him to clinch his first break.
The 36-year-old surrendered just three points on serve in the opening set and took control of the second with a crosscourt backhand victor that broke Chardy when tied at 4-4.
Chung, seeded 23rd in Indian Wells, defeated Pablo Cuevas of Uruguay 6-1, 6-3. I'm really sorry to the fans who wanted to see this match. "How good will still remain to be seen". On the very next point Martic hit a forehand wide as Halep took the game and a 5-3 set lead.
His next opponent on Friday will be Canadian Milos Raonic, who won by walkover when qualifier Marcos Baghdatis of Cyprus was unable to play due to a stomach illness. Chung has lost four of his last five quarterfinal matches.
His fellow 21-year-old, Borna Coric, also booked his quarter-final spot in the early proceedings on Wednesday as he prevailed 6-2, 6-7 (6), 6-4 over Taylor Fritz of the United States.
He will next face Juan Martin del Potro, after the Argentine beat compatriot Leonardo Mayer 3-6 7-6 (7/2) 6-3.
"I'm just start new team this year with Godwin Neville, and he made me trying to enjoy on the court", Chung said.
"I am surprised he came back so soon".
"But there is absolutely no guarantee that I would have a better chance now than before".
The 2018 French Open could be without Federer and Nadal with both men mulling over their involvement.
"Everything was a little bit off from my side", Pliskova said.