The east Londoners headed west in January last season, grinding out a 0-0 draw in a game which saw Chelsea fire 39 shots on the West Ham goal.
Jose Mourinho branded West Ham's style of play like "football from the 19th century" in the aftermath of the fixture, with Allardyce's men battling relegation at the time.
The point left West Ham 18th in the Premier League, but they head to Chelsea this time fourth in the table after a season which has seen Allardyce implement a free-flowing style.
And Adrian believes West Ham's potent frontline can help them become the first Premier League side to take something away from Stamford Bridge this season.
He told the London Evening Standard: "I think that this game on Boxing Day and this season is so different because we have many combinations and possibilities to attack - our football is different.
"Of course, we are away from home and we still need to be resolute but this time we have attacking players, we are fourth in the Premier League.
"This time we will go there and attack Chelsea. Why not? We want to get three points.
"This season we have different players and we have been able to play with more freedom. It is good because we have plan A, B or C. That is good for the team and the manager."
James Tomkins (thigh) is Allardyce's only injury doubt, though Mourinho could be without Eden Hazard after the Belgian attacker hurt his ankle in Monday's 2-0 win at Stoke City.
The Chelsea boss is not perturbed by fitness issues in the hectic Christmas period, however, and hailed English football's festive traditions.
"I have lots of respect for the players in this country, it doesn't matter English or not English," he said.
"But the moment you are in football in this country I respect them a lot. In this moment the German guys [Bundesliga players] are on the beach, the Spanish guys [La Liga] are in the Maldives getting the sun and everybody is doing that.
"In this country you play Boxing Day, you play on the 28th, you play on the 1st [of January].
"No family, no Christmas, just football and I think they deserve respect.
"The supporters all around the country they give them that respect by selling out every stadium and I think that is the way to do it with the professionalism every player has today."
