Check your spark plugs....they make a chirping noise when there loose.Or try to post a video of the noise.

 

Pull out the dipstick while at idle and tell me if the chirping noise stops.

 

I did it and the engine made it louder bro

 

Yea a video would be helpful. Can you tell where the chirping noise is located? Is it coming from the pulley area where the belt is? Mine use to chirp when I had to a/c on... they had to replace the harmonic balancer under warranty

 

My tensioner was chirping only right after starting and when it was cold out. Replaced it and the belt and I haven’t heard it since.

 

Start here:
2011-2016 Cruze 1.4 PCV Valve Cover/Intake Manifold Issues

 

LOOSE PLUGS, BAD DIAPHRAM IN THE PCV PURGE VALVE ON THE TOP OF THE VALVE COVER. v3.4 =GM PCV KIT FIXES THE VALVE COVER PCV FROM BREAKING AGAIN AT CRUZEKITS.COM FOR $79.00