Rice has backed the 18-year-old, who was on the score sheet in their 2-1 victory at the Emirates, to be a key player for his side.
"He 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," Rice said.
"I am sure that is something he will be working on because he's certainly not a stupid boy. From Arsenal supporters' point of view, they are going to be seeing a lot of this boy."
Oxlade-Chamberlain joined Arsenal from Southampton in the summer for a fee thought to be around £12m.