ESC and Traction Control light comes on 2011 HHR LS

Mel, This may not be a problem for you to take on, pretty sure it has to do with the SRS senors which could also cause B0140 code traction control possibly shut off by fault in SRS system. Take in to a good Technician for diagnoses. Check the attached links,instruction and guides, Good luck
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HHR OBD2 codes B0100 B0140 airbag and speed sensor Chevy HHR Network

What does error codes B0100 and B0140 indicate wrong on 2011 Buick...

2011 Impala LS ABS Stabilitrak Traction Control Problems Chevrolet Forum...

Check the engine codes first. Some codes will shut down the ESC and traction. Then Traction codes will shut down ESC. With out codes we just guess.

Check out this forum it might answer your question , check the answer from triplex-08.

Service Traction and ESC Archive Chevy Malibu Forum Chevrolet Malibu...

ECS is electronic controlled stability. It works with traction control when it is slippery and it does cause what you describe. It reduces the power to the engine and drive train. IT could be from ice build up on wheel sensors.

You will need to find the trouble code for malfunctioning wheel speed sensor. The Powertrain control module thinks that there is a wheel spinning or slipping, which in turns retards ignition timing to limit the slip. It could be a bad sensor or a broken wire harness. Some parts houses can give you the code, but you will either have to take it in to a Certified Technician, or diagnose it yourself if you are qualified.

Did you check for codes & google them,
to see what system has a possible fault

This is pretty common and is usually caused by metallic particles stuck to the magnetic encoder on the wheel speed sensor. GM has issued a service bulletin about it.
Service traction system service ESC Ricks Free Auto Repair Advice

you would need to scan the computer and see what codes you have to start this should still be under factory warr being a 2011 unless you have a lot of miles on it

the abs light is on because it is telling you that the abs system has a fault in one of the sensors, also with the light on it means that the abs is disabled. the traction control and esc are on because they are linked to the abs

I had this problem with my 2007 HHR. I drove away with the service engine and the service traction light on. The car was stuttering through the gears. I took it back and they checked it. They disconnect some wires while they change the oil and one was loose. The service engine turned off but the service traction stayed on. We disconnected the battery for 3 minutes and it fixed the problem. Some of those other guys spent up to 300 dollars to fix the problem. Hope it works out for you.