Chambers made 36 appearances for the Gunners last season, helping the side to an FA Cup triumph and impressed with a string of composed performances.
The 20-year-old proved his versatility, moving between the centre and the right hand side of defence after joining from Southampton last summer.
He also went on to win three caps for England after making his debut in September and said he did not expect to make so much progress so quickly.
“In a short space of time I think I have grown massively,” Chambers told the club’s website. “I have exceeded my expectations of what I thought I would achieve this season.
“I can only thank the coaches and the players for helping me do that and I just want to keep going, keep improving day by day to become the best player that I can be and be proud of myself.
“Playing for Arsenal is an achievement and so is playing in the Champions League and for England. I am really proud of myself and equally I want to go further and become the best player I can at Arsenal. I won’t stop working until I get there.”
Chambers said the prospect of playing for Arsene Wenger was one of the main reasons why he decided to leave Southampton for the Emirates last summer.
And he thanked the manager for the confidence he showed in him during his maiden season at the club.
“He has been fantastic to me, really supportive and he has given me an opportunity to play,” Chambers said.
“I am very grateful for what he has done. Everyone has expectations of things but for me he has exceeded all expectations of what I had.
“I can’t thank him enough. I think he is very thoughtful in everything he does and you know he gives everyone a chance and gets the best out of all the players, which is a very good quality as well.”