Holy Trinity Church, in the heart of the Old Town, is losing £1,000 a week and is expected to run out of money within the next four years if extra funding is not found.
Since taking over as vicar last year, Reverend Dr Neal Barnes has been looking at ways to generate extra income.
One of the ideas being looked at is creating a visitor centre inside the 700-year-old church, giving information about the sights in Old Town.
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