I've recently seen the same behavior in my 2009 Cobalt. It seems that the error code is describing a problem with the valve timing advance system. Autozone has a diagnostic procedure you can follow help isolate the cause.
In my case, if the engine starts to run rough at idle, I can move the wires on the intake valve camshaft position actuator (located near the 'front' of the engine, under the plastic engine cover, passenger side of the vehicle) to stop the problem. Once I stop the problem I can't make it re-occur by moving the wires. It immediately re-occurs if I remove the connector from the actuator, and resumes normal operation a few seconds after I reconnect the plug. After this 'treatment' the engine will run OK for a few trips and then the problem will return.
I haven't yet tried replacing the actuator, but I've replaced the oil since this occurred with no improvement. The symptoms really look like it is caused by an electrical problem, but I have not been able to conclusively determine if this is correct. The electrical resistance of the actuator is in the allowed range.
I may try tapping on the actuator at the next opportunity to see if that will help it resume normal operation. Otherwise, I don't know anything else to do but blindly replace it to see if that prevents the problem from returning.