The 51-year-old collapsed during the raid at an address on Wordsworth Crescent on 26 November.
Paramedics removed a package lodged in his throat and took him to the Countess of Chester Hospital for treatment. He died there on Friday.
Police said he was not restrained during the raid. Pathologists have yet to establish the cause of his death.
A post-mortem examination was carried out on Sunday, the results of which have been withheld pending reports.
Forensic tests to work out what the package contained are being carried out, said police.
A 50-year-old man who was also in the property at the time of the raid was arrested on suspicion of possession of class A drugs. He has since been bailed.
The matter has been referred to the Independent Police Complaints Commission for investigation.
A man who choked on a package during a police drugs raid at a property in Chester has died in hospital.