The 19-year-old moved to the Gunners from Southampton for around £16m earlier this summer, and the former Reds star thinks that the youngster has settled in quickly at the Emirates Stadium.
He told the Daily Mail: "Though the season is only two weeks old, Chambers has been Arsenal's outstanding player.
"He built on the promise of his first two performances with a commanding display against Besiktas in the Champions League on Tuesday.
"Chambers might only be 19, but he wasn't ruffled by the hostile atmosphere in Turkey and that experience will stand him in good stead for what awaits him on Merseyside. Everton play good football under Roberto Martinez and Goodison remains an intimidating ground."
Arsenal travel to Everton in the Premier League this evening.