Teenager Chambers made the move to the Emirates Stadium from Southampton in the close-season, and his form for his new club has resulted in him earning a place in Roy Hodgson's senior England setup.
Chambers started both of England's recent Euro 2016 qualifiers, and club-mate Szczesny feels the 19-year-old has demonstrated his quality with Arsenal.
The Polish goalkeeper told the club's official website: "It is a strange one because I would imagine that to be very successful at 19 you need to be massively confident, maybe overconfident at times.
"But Calum isn't - he's very humble, very quiet and he shows his confidence on the pitch. It is a massive quality because he looks very comfortable, whether you play him at right-back or centre-back.
"He is comfortable on the ball, he is comfortable defending and he is very strong as well. He has been a massive signing.
"The pressure was on him as well because he was 19, he came to a big club and he went straight into the starting XI but he has been coping very well."
