This museum is at 27 Grosvenor Street, Chester. I was pleased I visited it when I was in Chester last week. A modest size museum and free to enter, it has a thorough history of Roman Chester. There is also a room dedicated to the Viking period. Look out as well for the recreation of a town house covering domestic life from the 17th to early twentieth centuries.
We spent an hour and a half in the museum. I loved the place though, admittedly, I am an historian. I was accompanied by a non-historian - and he liked the place as well.