Q: My Mac has started to shut down unexpectedly since we installed google chrome. Any ideas?

Hi, lindafrommendota.  

Thank you for visiting Apple Support Communities.  

I understand that your Mac restarts unexpectedly after the install of Google Chrome.  Here is a troubleshooting article that will walk your through some steps for this issue.  However, since this issue started once you installed a specific program, I would uninstall this program and test the results.  

OS X: When your computer spontaneously restarts or displays "Your computer restarted because of a problem." 

Cheers, 

Jason H.