The 19-year-old completed his €20 million move from Southampton last week and was handed a start at centre-back as Arsene Wenger's side demolished the Portuguese champions at the Emirates Stadium.
"It's amazing. To play in front of such a big crowd with the quality of players I'm playing with now, it's a great achievement," Chambers told BT Sport.
"I enjoy centre-half, obviously I played at right-back last season but if there's an opening I'll try my best to grab that opportunity and take it.
"The quality of the players that we've got in this team is immense. To play with such amazing players is an honour, there's always an option on [for a pass].
"This club is destined for great things. It has been in the past and it's got a great history. I think we can do well in the league this year."
Four goals from Yaya Sanogo and a strike from Joel Campbell eased Arsenal to victory over Benfica, though Wenger was also keen to praise Chambers' display in defence.
"Chambers played well," said the Arsenal manager.
"He was intelligent and good in the air. What he did is very promising."