The 19-year-old produced another commanding display at the heart of defence on Tuesday night, helping the Gunners keep a clean sheet in the first leg of their Champions League play-off against Besiktas.
Szczesny is impressed by Chambers' versatility and thinks the defender has a bright future ahead of him at the club.
"He's been fantastic for us and adapted very quickly to being a centre back," Szczesny said.
"He only came in pre-season so he hasn't a lot of time to train with us in this position.
"You can't tell that he's only 19 years old, he looks like a very experienced centre back. He's doing very well at the moment."
The goalless draw in Istanbul means Arsenal remain unbeaten in Champions League qualifiers. But Szczesny believes the team need an improved performance in the return leg at Emirates Stadium next Wednesday if they are to progress to the group stages once more.
"We always want to play better and the only thing we can focus on is getting a result in the second leg," he said. "It doesn't have to be a pretty one but we want to get through and secure Champions League football.
"I thought it was very enjoyable. It was a fantastic atmosphere and a very tough game. It was exactly what you would expect from a Champions League fixture. It was a good test for us and we came out with a clean sheet which is a positive. We'll be confident going into the second leg."Copyright 2016 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source