Hill-Wood spoke out as Arsenal’s turnover broke the £200million (€285m) barrier after their move to the Emirates Stadium.
He said: “I don’t want to run Chelsea down, but one has to concede Manchester United and Liverpool are probably the biggest names in British football.
“For Chelsea to think they are suddenly going to dominate United and Liverpool is fantasy. It is not going to happen.”
Chelsea chief executive Peter Kenyon has spoken of his desire to “turn the world blue” — but Stamford Bridge has been rocked by the exit of Jose Mourinho.
And they attracted a crowd of less than 25,000 for last week’s Champions League game against Rosenborg at Stamford Bridge, Mourinho’s final game in charge.
Hill-Wood added: “I found it very surprising Chelsea had only 25,000 for a Champions League game.
“Our fan-base probably started in the 30s and it’s been handed down from father to son and so on. It takes 100 years to build and about 100 minutes to destroy. Money is irrelevant to history and how big your club is.”
Chelsea chief executive Kenyon recently out-lined the club’s plans to dominate the game under owner Roman Abramovich.
He said: “It’s building that dynasty. That’s what Roman wants to be part of, Chelsea becoming part of Europe’s dynasty.
“Over a 10-year period, you need two European Cups to be a world club. You have to dominate your domestic league. We have to have an infrastructure to deal with that and people to deal with it.”
Arsenal insist their financial strength demonstrates they have no need for new overseas investment, and hope to fight off any new moves by Russian billionaire Alisher Usmanov, who is aiming to increase his 21% shareholding.
Usmanov wants to gain a 25% “blocking stake”, which would make the corporate running of the club more difficult without his backing.
Hill-Wood said: “I don’t think Roman Abramovich has helped the Russian cause. The board at Arsenal is completely united and has no intention of not remaining so.
“The idea of us selling out to whoever is simply not on the agenda.”
In an open letter, he also urged Arsenal’s shareholders to think carefully before selling any of their shares.