Already 2-0 down after just seven minutes, Oxlade-Chamberlain threw a hand at an Eden Hazard shot that was going wide and referee Andre Marriner pointed to the spot.
He then proceeded to send off a bewildered Gibbs.
Hazard converted the penalty for the Blues and put the game effectively out of sight for the Gunners on the occasion of Arsene Wenger's 1000th game in charge of the north London side.
Even more bewildering concerning the sending off was the fact that Oxlade-Chamberlain seemed to tell Mariner that it was him who had handled the ball.
Former Chelsea player Pat Nevin said on BBC Sport:
I feel quite sorry or the referee, who didn't see it.
But Alex Oxlade-Chamberlain was telling him it was him.
Use a bit of common sense, surely? They were right to send someone off, it was right to give a penalty, but they just got the wrong man.
According to BBC Radio 5 live, Marriner admitted to sending off the wrong man at halftime:
Meanwhile, BTV reports it was simply a case of "mistaken identity":
Confusion abounded at the time of the incident as the referee took several moments to give the penalty and produce the red card.
After the match, Chelsea manager Jose Mourinho talked about the bizarre decision, according to Daniel Taylor of The Guardian and Miguel Delaney of ESPN:
Rob Harris of the Associated Press reported the Premier League's statement on the red card:
Gibbs will likely receive no ban as the card should certainly be overturned.
However, the fallout will be of little comfort to Arsenal's players and fans as with only 10 men on the field and a 3-0 deficit to make up the game was effectively over in the first quarter of the game.
Arsenal were looking for a victory that would have taken them within one point of table-toppers Chelsea with a game in hand.
However, a loss puts them seven points adrift of the west London side and the FA Cup is looking the most likely target for Arsenal to pick up their first silverware since 2005, a feeling compounded with Oscar putting Chelsea 4-0 up just before half-time.