Costco – Chester – Opening Hours & Store Details Costco is found in an ideal space in Dunkirk Trading Estate on Gates Ln, approximately a 3.96 mile driving distance north-west of the centre of Chester, in Gates (nearby Chester Gates Industrial Estate). This store is situated in a convenient location for people from Moston, Backford, Westwood Park, Great Sutton, Mollington, Capenhurst, Stanney Oaks and Lea-by-Backford. This page will give you all the information you need about Costco Chester, including the hours of opening, address details, direct number and further details.