Pepe has scored 16 goals this term.
Pepe scored twice as the Gunners beat Brighton 2-0 on the final day of the Premier League campaign.
The win was not enough to seal European football for Arsenal, who finished eighth for the second year in a row.
But the 10,000 returning fans at the Emirates Stadium were treated to two well-taken second-half goals as Pepe continued a fine run of form.
The Ivory Coast winger has divided opinion since his £72million move from Lille in August 2019 but has lately answered the call of manager Mikel Arteta to show greater consistency in his game.
Pepe ended the campaign with 16 goals and has notched nine times in his last 13 Premier League starts.
Asked if Pepe can be at his best next season, Chambers replied: “Yes.
“I think he’s on good form at the minute and he’s been playing really well and scoring good goals and his confidence is high.
“We’ve seen that all along and we’ve known the quality that he’s had and it’s just really nice to see him show everyone else what he can do.
“(His performance was) brilliant. He was covering me defensively, which is amazing.
“I think he’s improved a lot, he’s a great player and we’ve seen it from the start in the first day of training, we’ve seen his quality, and I think now he’s really starting to show everyone what he can do. We’re all delighted for him.”
Chambers also admitted the season had not turned out the way Arsenal would have liked, with no silverware to soften the blow of a poor league campaign.
“Obviously very disappointing,” he told arsenal.com when asked about missing out on European qualification.
“I think we are disappointed with the season as a whole, it’s not where we wanted to finish and be.
“Obviously we need to focus on that next season and we need to change, but despite that we’ve finished the season strong, so there’s some motives to take into next season.
“We will take the momentum with how we’ve finished the league and take that into the start of next season.”
Arsenal’s fifth straight league win was a fairly comfortable one as Brighton offered little in the way of attacking intent.
The Seagulls went into the game on the back of a surprise victory over champions Manchester City just five days earlier and skipper Lewis Dunk felt those exertions played a part in an insipid display in north London.
“We weren’t good enough in the first half, maybe a little bit better second,” he said.
“That’s one of the only performances where we haven’t been at it this season and it’s frustrating.
“The boys put a lot of effort into the game on Tuesday, but we weren’t at it on Sunday.”