Arsene Wenger's assistant believes the 18-year-old can follow in Theo Walcott's footsteps and become a hit for club and country after making a goalscoring European debut
The former Southampton teenager has made a bright start to life in north London, scoring in the League Cup against Shrewsbury and also on his European debut against Olympiakos this week.
Chamberlain has been compared to Theo Walcott and Rice believes that Oxlade-Chamberlain would do well to look up to his fellow Southampton academy graduate.
"From Arsenal supporters' point of view, they are going to be seeing a lot of this boy," Rice told reporters.
"He has a big, big challenge to now get in front of Theo. I know that Theo is a very strong-willed guy as well and he won't give in easy. It all bodes well for England anyway.
"Alex can go inside, he can go outside, he's got that injection of pace and I think what he needs now is to be consistent in his play. I am sure that is something he will be working on because he's certainly not a stupid boy.
"He has good people around him and they are telling him all the right things. Alex is very friendly with Theo and no doubt he will give him the benefit of his experience as well."
The 18-year-old impressed during Arsenal's 2-1 Champions League win over Olympiakos on Wednesday night.
Rice has insisted it was a tough game for the Gunners and that they were pleased to have come away with a victory that leaves them second in Group F behind Marseille, who they will play next in the competition.
"You can't turn around and say we had all of the game because that would be unfair," he said.
"The first 20-25 minutes we were really in it well, but after that for about 15-20 minutes we maybe lost our way and they came back into it. From a defender's point of view, the goal was really poor. Second half we had to knuckle in, fight and get our shape right.
"It is unfortunate we didn't get the third, but we also had opportunities on breakaways in the second half. They came, they waited for us, they broke us up in the middle of the park and in fairness they did well."