2007 Chevrolet Cobalt Rattling

Is the rattle coming from underneathe the car? Or under the hood?

If underneathe the car, raise it on a lift and have someone to rev the engine as you and a partner looki for the sorce of the noise.

Things to check;
The metal cover to the catalytic converter.
The heat shield above the exhaust pipe (they attach to the bottom of the floor board)
Engine and transmission mounts
Exhaust pipe hangers
Muffler

Check these:
the cover on the exhaust manifold.
The belt tensioner (with a partner revving the engine, watch the tensioner to see if it vibrates excessively, causing the noise you hear).
The plastic engine cover
oil dipstick
check to see if the engine moves excessively when it is revved (loose or broken motor mount).

Sounds like a bad wheel hub bearing assembly. The sound increase or decreases with vehilce speed. Try getting up to around 35 mph when the sound is very noticable, put the car in neutral and see if the sound remains (and changes with vehicle speed). This is a good indication of a faulty wheel bearing.

If that's the case, raise that wheel an try shaking it (with a hand at the 3 and 9 o'clock positions and then again with hands at 12 and 6 o'clock). If there is wobble, suspect the wheel hub bearing. However, check for wheel lug tighness and hub center bolt tightness as well.