Oxlade-Chamberlain made a £12million move from Southampton this summer and had been earmarked for a slow integration in to the Gunners first team.
A series of injuries, most recently to Walcott, have given the 18-year-old a chance to shine, however, and he has grabbed the opportunity with both hands, scoring in his first start against Shrewsbury and bagging the opener in last night's 2-1 win over Olympiacos.
The Greeks had little answer to the former Southampton winger's pace and the goal - a 20-yard drive that went in off the post - shows the youngster has an eye for goal too.
After the win, Arsenal assistant manager Pat Rice tipped Oxlade-Chamberlain to be a future star for club and country, and the player himself says he will only get better if he has more minutes on the pitch.
Walcott enjoyed almost instant success when he, like Oxlade-Chamberlain, moved to the Emirates Stadium and has since gone on to win 18 England caps.
Oxlade-Chamberlain admits it will be difficult to take the 22-year-old's place on the right flank, but is up for the challenge.
"It'll be very hard for me to get Theo [Walcott]'s position or anyone else's but I am up for it," Oxlade-Chamberlain said.
"I have got confidence in my ability to [make an impact this season] and I think one of the main things with me is that I am going to learn by getting more game time.
"I know that isn't going to come easily but over this season, next season and the one after I am just going to build on it and work hard and train.
"I am always learning things from the boys in training because they are quality players and that's it for me. Getting stronger and fitter by playing games is only going to help me.
"You are all mates off the pitch but on it you are all competing for places. I think that only makes a healthier squad - more players fighting for positions can only mean everyone has got to step their game up."
Walcott missed last night's Group F win with a knee injury but could return for Sunday's north London derby at Tottenham.
Oxlade-Chamberlain is looking forward to the hotly-anticipated match - which last year ended 3-3 - regardless of what role he plays.
"I have never played in a derby," he said. "The closest I got to was Southampton v Bournemouth but that was more of a derby for Bournemouth rather than Southampton fans.
"Just to be involved in the squad in any game, I am honoured to do that. If I am on the bench or in the starting line-up, I'll be happy to be there."
Arsenal tracked Oxlade-Chamberlain for some time before finally signing the winger at the start of August.
Manchester and Liverpool were also linked with him, but Oxlade-Chamberlain was quickly won over by the Arsenal playing philosophy and the reputation of manager Arsene Wenger.
"I always used to watch Arsenal and I loved the way they played football," he said. "It was the manager, stadium and fans that sold it for me.
"The boss is a massive influence and such an intelligent man. Even in his team-talk last night, the stuff he says is brilliant. You always learn from him. He has a quiet word now and again but what he says is spot-on.
"He's just a fantastic man and the way he thought he could develop my game pushed me towards Arsenal. It's a massive club. I came to a few games last season - the Barcelona one here when they won - and I was blown away so that was it."