Sounds like it's behaving normally
Page 4-20 of the 2009
Vibe Owner's Manual says this about the Check Engine Light (Malfunction Indicator Light)
This light comes on when the ignition
is on, but the engine is not running,
as a check to show it is working. If it
does not, have the vehicle serviced
by your dealer/retailer.
If the check engine light comes on
and stays on, when the engine
is running, this indicates that there
is an OBD II problem and service
is required.
I guess one way to think of it is that with the ignition on and the engine running, the light is saying check the engine because it seems to not be running. It will stay on forever if you leave it in On with the engine not running
I know on some cars I've owned there was a way to perform a ritual of switches and things, or jumpering a connector somewhere to to get a light to flash out a code, but Vibes don't do that. You need to use an ODBII scanner. Most chain auto parts stores will use one to check for codes for free.
But on yours, the light goes out when you start the engine, so I'd assume there are no codes to be read.