The 29-year-old Scot, who has been formally recognised by the Queen for his services to tennis and charity, brushed Chardy aside in a 20-minute first set before triumphing 6-0, 7-6 (7/2) in Doha.
The victory extended his career-best winning streak in competitive matches to 25.
Murray will play Gerald Melzer in the next round after the Austrian beat Paul-Henri Mathieu 6-7 (2/7) 6-3 6-2.
The Scot said he was “pushed to the end” by world No 69 Chardy.
“He didn’t start well,” said Murray, a three-time finalist in the tournament. “It’s always difficult, the first match of the year. Both of us were probably feeling a bit nervous. In the second set he played well. He was a lot more aggressive.”
France’s former Australian Open quarter-finalist had rallied to ensure a contest in the decider, but his poor performance on the return of serve led to his early elimination from the hard-court tournament.
At the end of a defining year in which he won his second Wimbledon title and another Olympic gold medal, Murray beat fierce rival Novak Djokovic in London to conquer the ATP World Tour Finals for the first time and secure the year-end No 1 ranking.
Last week he recovered from an exhibition defeat to David Goffin in Abu Dhabi to beat world No 3 Milos Raonic in straight sets and he stepped up a gear – or two – last night in Qatar.
Chardy, whose sole victory in nine prior meetings with Murray came at the 2012 Cincinnati Masters, was helpless to resist the Scot’s serve in a lightning opening set.
The world No 69 upset the match’s momentum by breaking Murray in the first game of the second set and an improvement on his serve saw him reach 3-3 for only three double faults.
Chardy looked keen to force a third set and composed several thrilling rallies on his way to the tie-break, but ultimately Murray’s tireless counter-punching and wide range of shots got him over the line.
Now Gerald Melzer lies in wait for the Scot. The Austrian left-hander, who defeated Paul-Henri Mathieu 6-7 (2/7), 6-3, 6-2 to reach the second round, has never played Murray before.
lRafael Nadal’s mission to add to his 14 grand slam titles in 2017 received an early boost as the Spaniard saw off Alexandr Dolgopolov in straight sets at the Brisbane International.
The 30-year-old world No 9, without a major prize since he won the French Open in 2014, needed only an hour and 16 minutes to dismiss Ukrainian Dolgopolov 6-3, 6-3 in Queensland in his first match of the year.
Nadal, seeded fifth on his debut appearance at this hard-court tournament, will next face Mischa Zverev.
Standing in the way of British hopeful Kyle Edmund is Lucas Pouille, through to the second round following his victory over fellow Frenchman Gilles Simon.
lAt the Chennai Open, Aljaz Bedene made a strong start to 2017 by beating Guillermo Garcia-Lopez in straight sets to reach the second round.
The British No 4 needed only an hour and 15 minutes to defeat the unseeded Spaniard 6-3, 6-3, setting up a last-16 showdown with Martin Klizan of Slovakia. Twenty-seven-year-old Bedene, who reached the French Open third round last year, fired seven aces.
lAustralia’s hopes of retaining the Hopman Cup ended after a tense three-set defeat to the Czech Republic allowed the United States to book their place in the final.
The pressure was on Nick Kyrgios and Daria Gavrilova ahead of their meeting with Adam Pavlasek and Lucie Hradecka in Perth after American duo Jack Sock and Coco Vandeweghe put themselves on the verge of securing top spot in Group B with a comprehensive victory over Spain earlier in the day.
All seemed to be going well for the hosts when Kyrgios wrapped up a 7-5, 6-4 win over Pavlasek, before Gavrilova surrendered a first-set lead to lose 4-6, 6-4, 6-4 against Hradecka.
The Australians took the opening set of the doubles match but, under the Fast4 Tennis format, they eventually lost 3-4 (5/1), 4-3 (5/1), 4-2.
That result gave Americans Sock and Vandeweghe an unassailable lead at the top of the group and a spot in Saturday’s final following their clean sweep win over Spaniards Feliciano Lopez and Lara Arruabarrena.