Check Engine and ETS Lite on on 2006 Chevrolet Cobalt SS

The 2 Lites came on and remaind on when I got home turned off car restarted car an hour latter ETS lite was off but Check Engine still on.

To properly diagnose a Check Engine light the use of a Scanner needs to be used to inspect and retrieve any stored trouble codes in computer system. Your local Dealer or you local repairs shop should perform such inspection and give you a report of what is causing Check Engine light to be on.
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Mine did the same thing, but it shut off and then when I went to restart it, it wouldnt start. So I wait 10 mins and try it again and it started, but the light was still on went home and waited an hour and started it back up and the light was off. I really dont know what happened.