A passenger, a man in his 50s, sustained life-threatening injuries in the incident.
A 22-year-old man from Walsall has been arrested on suspicion of causing serious injury by dangerous driving after the incident on Tuesday evening.
It happened at just before 11pm when a dark blue Vauxhall Corsa failed to stop for officers in Banbury town centre.
The vehicle joined the A4260 at speed, travelling towards Oxford. While overtaking another vehicle on the approach to the junction with the B4100, Aynho Road, and hit a stone wall.
As mentioned, a man in his 50s sustained life-threatening injuries and remains in hospital. A second passenger, a woman in her 40s, sustained minor injuries and was taken to hospital but has since ben discharged.
Investigating officer, Sergeant Naomi Hames, of the Roads Policing Department, said: “I am appealing for witnesses to this incident, which resulted in three people sustaining injuries, one of which, a man in his fifties, sustaining life threatening injuries.
“I would like to appeal to any other drivers who were using this road at the same time as this incident on Tuesday. Did you see a dark blue Vauxhall Corsa, or did you see this incident taking place?
“We would like to hear from anyone who has any information in relation to this incident.
“Please contact Thames Valley Police on 101, quoting reference number 43200290289.
“Reports can also be made online, or you can call independent charity Crimestoppers on 0800 555 111.”