Paramedics and police were called after reports that a woman had died in Redhouse.
Emergency crews were called to a property in Millgrove Street at around 9am on Friday, July 10, with police called by the ambulance service.
She was pronounced dead at the scene.
The circumstances are not thought to be suspicious and Wiltshire Police said a report would be prepared for the coroner.
Her family have been informed, a spokeswoman for the force said. "Our thoughts are with them at this difficult time."
The Wiltshire Air Ambulance helicopter was also called to the incident.
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