The Robins come to St Mary's in round three of the competition without a league victory to their name this season, although they did knock top-flight Crystal Palace out at the previous stage.
Mauricio Pochettino made wholesale changes to the side for Saints' second-round rout of Championship side Barnsley, and make take a similar approach against tomorrow's third-tier opponents.
18-year-old Chambers is one player who could profit from such a reshuffle, having lost his place to Nathaniel Clyne for the side's two most-recent Premier League matches.
And, if selected, the England Under-19 captain will not be taking this evening's match lightly.
"Bristol will come here wanting to prove a point and looking for an upset, so I think we have to play with respect to them," Chambers told Saints Player
"Hopefully our quality will come through in the end. We have good a really squad now. In training the quality is so high that everyone is improving week-by-week.
"With Nathaniel fit, we'll both be pushing each other on," continued the youngster. "There's great competition for places in the squad now, so we'll be improving each other's games.
"If I play [against Bristol City], it's another opportunity for me to show what I can do and to try to really push on."
Chambers made his Southampton debut in the League Cup a year ago, appearing as a substitute in a second-round win over Stevenage last season.
Fellow Academy graduate James Ward-Prowse also made his first appearance for the Club in the competition in the 2011/12 campaign, while Harrison Reed, Omar Rowe and Jake Sinclair came off the bench to make their debuts at Barnsley last month.
And Petersfield-born Calum says he's enjoying playing in the First Team alongside players who he has progressed through the youth ranks with since joining the Club a decade ago.
"Southampton have this great philosophy of bringing through young players – you saw that in the opening game, when we had three 18-year-olds on the pitch and we got a 1-0 win away at West Brom," he explained.
"It's quite funny playing with [Ward-Prowse and Luke Shaw] because I've been with them since I was about seven years old, when it was our dream then to come through and play for the First Team.
"It's such a good feeling to know that all of our hard work over the years is finally paying off. We're so proud of ourselves for getting there."