The 18-year-old earned his first Premier League appearance against West Brom in the club's season opener in the absence of regular right-back Nathaniel Clyne.
The youngster has kept his place in the side after impressing during that 1-0 victory last month and is delighted with how the new campaign has unfolded on a personal level.
"It's been quite a mad first month to be honest, I've enjoyed every minute of it, getting games under my belt for the first team which is what I was aiming to do at the start of pre-season," he told SaintsPlayer.
"When you get the chance you have to take it and everyone knows that, and I felt that when I got my chance I took it and I just want to keep pushing myself on and striving to do the best I can.
"During the game (against West Brom) you’re trying so hard and when the final whistle went it was the best feeling I have ever had, I think I went round hugging everyone, going mad.
"It was just the best day of my life probably."
Chambers - who like Luke Shaw and James Ward-Prowse is an academy graduate currently challenging for a first-team spot - will face stiff competition from Clyne, though, to remain in the Southampton side.
The 22-year-old, who signed from Crystal Palace in July 2012, made 34 league starts last season.
Chambers welcomes the challenge and is focussed on beating West Ham in the first game after the two-week international break on Sunday.
"Everyone is fully focused on West Ham, we're looking at how they play and just trying our best really," he added.
