Officers had attempted to halt a silver Mercedes on New Crane Street shortly before 2pm.
The car failed to stop so officers – supported by the police helicopter – followed it through the city before ending the pursuit due to "the manner of the driving".
The vehicle was found abandoned on The Groves and two men – aged 22 and 23 – have since been arrested on suspicion of both drugs and driving offences.
A Cheshire Constabulary statement said: "At 1.53pm officers attempted to stop a silver Mercedes on New Crane Street, Chester.
"The vehicle failed to stop so officers, supported by the National Police Air Service, followed the vehicle as it travelled through the city.