The Gunners take on Sunderland on Saturday afternoon.
The Gunners are the current holders of the competition, having won it for the last two years running.
They are now aiming to become the first team to win it for three years running since 1886, and they will come up against relegation-threatened Sunderland on Saturday.
And Chambers says that opportunity to make history is giving Arsene Wenger’s squad an extra incentive this year despite them focusing on winning the Premier League.
“It would be an amazing achievement [to win it for the third time in a row] and I’m sure everyone will be everything to get there,” he told arsenal.com.
“ I wouldn’t say we are discussing it but we are thinking about it. Anything in the cup can happen, it is not always straightforward.
“You have to have both short range and long-range goals. A long-range goal would be to break records, win trophies and do well, so I think everyone strives for that.”
While winning the FA Cup is sure to be a massive incentive to Arsenal this season, it will surely be far down in their priorities.
They are currently sitting top of the Premier League table, two points ahead of Leicester City, and will feel that this is their best opportunity to win the league in a number of years.
Winning that would be a bigger success than a third FA Cup triumph, and despite the temptation to make history; the competition could be sacrificed to help ensure the title ends up at the Emirates.