The "Roman Garden" monicker is something of a misnomer. Certainly there is no indication that a garden existed on this site near Newgate during Roman times. The garden space was, in fact, assembled in 1949 from bits and pieces of Roman artifacts found throughout Chester. The project was initiated as Chester's contribution to the 1951 Festival of Britain.
The gardens contain Roman columns and a "hypocaust" or underfloor heating system. Today it is less a Roman archaeology attraction than a quiet green space in the city centre. It makes a nice stopping off place if you are walking the old city walls of Chester.