Simon Byrne saw members of the public trying to free passengers after a serious crash on the A550 in Two Mills on the evening of 25 January.
He activated the blue lights on his force BMW but, as he pulled in, another car hit his "at slow speed".
Cheshire Police has admitted liability for the damage caused.
A number of pedestrians were in the road and debris was spread across both carriageways, police said.
Mr Byrne, who was off-duty at the time, reported both the initial and subsequent collisions and carried on assisting those at the scene as they lifted damaged traffic lights off a car to try to free injured people trapped inside.
When officers arrived at the scene, they breathalysed Mr Byrne. The test was negative.
Following the crash a review found all officers at the scene acted appropriately.
The chief constable is provided with a BMW X3 Compact SUV as part of the terms and conditions of his contract.
It is not a marked police vehicle, but does have blue lights fitted in case the car is used in an emergency.
The Chief Constable of Cheshire Police caused a second accident when he stopped to help at a crash scene, the force has confirmed.