The Gunners kept a clean sheet on the final day of the Premier League season, defeating Brighton 2-0 at home.
Pepe got both goals for the London club, but Chambers was also impressed with how the winger put in a shift defensively to help his teammates.
Asked about Pepe, he told reporters, per the club website: "Brilliant. 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."