Walcott hit a superb treble in victory over Newcastle United.
"He bangs them in for fun in training," said Oxlade-Chamberlain. "Someone with pace is a nightmare to defend against. When he gets the service, he can punish teams. In training, he's no different.
"When Theo first came, he was training with players like Thierry, (Dennis) Bergkamp and (Robert) Pires. He's learned from the best, he's getting better and better, and there's no one better to learn from.
"From the player that I first started watching to the man he is now, he is only getting better and better and he's still only 23.
"He's got such a mature head on his shoulders. He's great on and off the pitch so he's so important for us. He was great for me when I first arrived. He took me under his wing, helped me. 'When he came along, it must have been even more daunting because I think Ashley Cole was the only English player around at the time.
"They had experienced players like Henry and Bergkamp. It must have been daunting so he realised it must have been hard for me coming in. So he helped me through that.
"He was the first person to really help me. 'I sit next to him in the dressing room and he's been really good for me."