Chester City Centre is an area of "Archaeological Importance, one of only five such designations in England", while the Rows are considered of "national and international significance because of their "age, extent and rarity".
Figures show there were almost 250 incidents of public urination last year throughout the city. Those caught urinating include an engineer, teacher, solicitor, footballer and "full time mother".
In an attempt to tackle the heritage crime, the council has started operating a "walk of shame" at 4am for people caught on CCTV urinating.
Rather than being charged and sent before magistrates, louts can instead choose to walk the streets accompanied by council workers to "experience the offensive mess and smells created by late-night revellers who use the city centre as a public lavatory".
Councillor Hilarie McNae, the council's Heritage Champion said: "Regrettably, public urination is a problem affecting every town and city centre - the added dimension in Chester is that it is destroying the very fabric of our world-famous Rows.
"We are working hard to raise awareness of the irreparable damage it is doing."
Sgt Andy Burrage, from Chester Inner Neighbourhood Policing Unit, said: "Urinating in public, particularly on the Rows, is not just anti-social, it damages the fabric of the Rows and leaves unpleasant odours for people using the area by day."