The environmentalists also hoisted a sign onto the balcony of the club, renaming it the headquarters of "Frack and Go", a fictional company set up by the demonstrators.
They also set up a live webcam dedicated to the anti-fracking protest in Knutsford, the main town in the Chancellor's Tatton constituency.
The protest has not gone down well with employees of the Conservative HQ.
Greenpeace environmental campaigner, Lawrence Carter, told the Huffington Post UK: "One of them ripped down one of the signs we'd put over the conservative club sign which said "Frack and Go".
Despite this, Carter said police seemed to be allowing the demonstration.
Chief Inspector Paul Carroll, of Cheshire Police, said: "The priorities for the constabulary are the safety of all parties, the facilitation of peaceful protest, that disruption is minimised and crime and disorder is prevented."
Protestors hoist up their sign onto the Conservative club
A statement on the Greenpeace site said: "Fracking is a dangerous gamble that will threaten local environments, derail efforts to tackle climate change and cost green jobs and investment.
"Across the street from his office is a beautiful village green where teams of activists have constructed a huge fake fracking operation - to show the Chancellor what his gas nightmare will look like."
A Greenpeace spokeswoman at the scene said two protesters had gained entry to a first-floor balcony at the Conservative offices and unfurled a banner emblazoned with Frack&Go - the branding of a fictional company set up by the organisation as part of its campaign.
The spokeswoman, who declined to give her name, said the group numbered about 25 and were being well-received by Knutsford residents and morning commuters through the town.
The fake platform set up by Greenpeace on the green
"We have got two climbers that have occupied the balcony on the first floor and have hung a Frack&Go company sign off the side of the building," she said.
"We've also fenced off the village green and set up a fake drilling rig and got a bunch of people acting as surveyors around the place.
"It's just really to bring home the reality to local people because there are actually two exploratory drilling licences that have been issued for Tatton so this the future they can expect.
"The guys have got no plans to move any time soon. The police are down here but we're just talking to them.
"A trustee of the village green has been over and he thinks it (fracking) is a good idea because he thinks it will bring down bills but it will not bring down bills and that's the message we are trying to get across."
Carter, said: "Fracking is an unnecessary practice. We don't need fracking, we don't need shale gas when we have got low-carbon forms of energy which not only deliver but also help the economy by delivering growth."
Fracking, or hydraulic fracturing, involves pumping water and chemicals at incredibly high pressure into holes drilled into shale rock.
This releases pockets of gas trapped in the rock which is then extracted.
Two earth tremors in Blackpool in 2011 were blamed on fracking leading to a temporary ban whilst the government conducted a review.
The technique was subsequently deemed to be safe although it still has many critics.
Monday's protest came with the release of a ComRes poll, conducted on behalf of Greenpeace, which found that 12% of people in Tatton who voted Conservative in the last election would be less likely to vote Tory again if fracking went ahead in the area.
"It seems George Osborne is so wedded to his dash for gas that he's willing to ignore the views of his own constituents," Mr Carter said.
"It's time the Chancellor stopped trying to play the JR Ewing of Cheshire and concentrated on investment in clean, safe, renewable technology that will create longer term jobs and a more stable economy."
All pictures via Steve Morgan/Greenpeace/Knutsfordtimes.com/PA