The incident took place at 9.55pm on Monday, April 5 on Westminster Road.
An unknown man approached the 85-year-old and grabbed hold of the bag he was carrying before leaving the scene.
The elderly man fell to the floor and received minor injuries to his hand, which required hospital treatment.
The suspect is described as being around 5ft 8in in height.
Police have been conducting a number of lines of enquiry and are appealing for CCTV footage of the area and any witnesses who may have information to come forward.
Detective Sergeant Simon Owen, from Chester Local Policing Unit, said: “While we have been following a number of enquiries I am appealing to anyone who has information and not yet spoken to police to contact us.