People living at the picturesque seaside resort of Aldeburgh in Suffolk say they already have enough places to shop. But Tesco say they believe the new store would provide people with more choice.
Tesco says the plans are for a small express store, which would provide basic groceries and create new homes and jobs.
Aldeburgh town clerk said: "We would fight vehemently against anything that would take trade away retaining the independence of our high street. However we do have to have a better understanding of what the people of Aldeburgh, our residents and our electorate want."
The proposed site for the Tesco is next to one of two Co-ops in the town. At the dry cleaners opposite, opinion was divided.
Donna Smith, of Danes dry cleaners, said: "Yeah I'd be for it because I use Tesco anyway, as I find lots of their things are cheaper than the Co-op or Asda."
Sarah Somerset, a resident, said: "I've personally never shopped in a Tesco and don't want to start now because because I think we are quite happy with the shops we've got."
In a statement, Tesco said: "This is an excellent opportunity to bring an empty site back to use... We open new stores where we believe they will be busy and popular and provide people with more choice."