can it auto-rotate on one rotor
No.
I think you may have a misunderstanding as to how the Chinook works. It is twin engined and tandem rotor'd.
But the engines go into a gearbox providing power to both rotors. So, either engine and both engines power the blades (via the gearbox). If one engine fails, the remaining engine automatically takes up the power, feeds power through to the gearbox thus still turning both sets of blades. Even if both engines failed, both sets of blades will still go round under autorotation (so long as you dump the lever quick enough!). I take it you arent a helicopter type of chap?