The second seed, a losing finalist last year, took just 53 minutes to reach the third round with a 6-2 6-1 thrashing of the Frenchman.
Chardy upset Federer in Rome last year but his hopes of a repeat win were not helped when a double fault gifted an early break.
Federer was displaying excellent touch on the clay and he coasted across the orange surface and was happy to get to the net, cushioning one backhand volley into the open court.
A terse exchange with the umpire appeared to unsettle Chardy and his mood darkened further as Federer snatched another break to claim the first set.
Chardy???s gloomy demeanour was briefly lifted when he broke back at the start of the second, but Federer would inflict more anguish with his full repertoire.
Preserving his serve with a dipping backhand, the world No 2 then opened a dominant 5-1 lead with a booming overhead.
Federer finished the job by lashing a forehand past Chardy and will face either Gael Monfils or Alexandr Dolgopolov in the next stage.
Earlier on centre court, Stan Wawrinka started the defence of his title with a 6-1 6-4 victory over Juan Monaco.
The seventh seed had suffered early exits at Indian Wells and Miami, but showed no signs of vulnerability as he broke twice for a 5-1 lead.
After conceding only two points on his serve in the opener, Wawrinka was made to work harder in a second set featuring five breaks of serve, eventually earning a third round clash with Grigor Dimitrov.
“The past two months were really difficult, both with my game and confidence,” he said.
“But I have much ambition for this clay-court season. I grew up on this surface and it’s easier for me than for other players to switch to clay.”