Hawes in Upper Wensleydale has a population of just over 1,000.
There is only one petrol station in the town, and it has higher pump prices than other locations that already receive a discount.
If it were to close, drivers say they would face a 34-mile round trip to fill up.
That's why it's been chosen as one of 10 areas that could benefit from a 5p-per-litre fuel duty cut.
Chief Secretary to the Treasury Danny Alexander said: "As a Highlander, I know all too well that fuel prices tend to be highest in areas where a car is needed the most."
More top news
Nutmeg was taken in as a five-year-old stray 26 years ago - and is still going strong despite recent health issues
Highways England has said it aim to have Northbound A1 reopened by 6am Wednesday after a large sinkhole formed overnight.
Chancellor George Osborne will seek to reassure financial markets on Monday morning following Britain's decision to leave the EU.