The 19-year-old joined from Southampton last month and has caught the eye with his pre-season performances before being picked out by Arsene Wenger as one of the best players in Sunday’s FA Community Shield win over Manchester City.
And the former England U19s captain says he’s now aiming to break into Gareth Southgate’s Under-21s squad, if not the senior set-up.
"That’s what I’m aiming to do and that’s my ambition," he told TheFA.com after the 3-0 win at Wembley.
"Only time will tell what happens now, but I just want to play as well as I can for my club and see what happens."
Chambers has featured in a number of positions for Arsenal in his early appearances, playing in midfield or at right-back before taking up a central defensive role in the Wembley showpiece.
And Chambers believes he’s learning more and more every day just by training and playing with the Arsenal squad as they prepare for next weekend’s Premier League opener with Crystal Palace.
"I’m really enjoying my time here, everyone has welcomed me really well," he added.
"It’s been quite a whirlwind of a few weeks but I’m taking every day as it comes and trying to concentrate on what I do.
"I just want to play the best I can and show everyone what I can do.
"We’ve got a lot of quality players here and the team spirit is really high at the moment, I think we can do well this season if we go into every game and give it 100 per cent."
Arsenal defender Calum Chambers speaks after The FA Community Shield at Wembley