The break-in happened just after midnight on Tuesday 4th September and money was stolen from the premises.
The cathedral's acting dean, Jane Brooke, said the damage to the four stained-glass windows which date back to 1920 was very upsetting, in particular, the damage caused to a window depicting St. Werburgh, the patron saint of Chester.
The damage caused to the cathedral is likely to exceed £10,000.
A 36-year-old Chester man has since been arrested in connection with the incident.
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