Harrison Reed, Omar Rowe and Jake Sinclair came off the bench to make their debuts at Barnsley last month.
Chambers told the Saints website: "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.
"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."