Cotherstone is a village and civil parish in the Pennine hills, in Teesdale, County Durham, England.Cotherstone lies within the historic county boundaries of the North Riding of Yorkshire, but along with the rest of the former Startforth Rural District it was transferred to County Durham for administrative and ceremonial purposes on 1 April 1974, under the provisions of the Local Government Act 1972. Cotherstone cheese is a celebrated delicacy, and the village was famous for it by at least 1858.