Google Chrome will damage your computer

How is your gatekeeper set up?

>System Preferences...>Security & Privacy

if the Allow Apps download from: is set to anywhere than any application that does not have an identity recognized by Apple will be prevented from running. If you have it set to "anywhere" it won't care who the developer is. Google is an identified developer and it's identity though Apple is very complicated to fake for someone trying to fool you, but if you do have a phony chrome on your system and anywhere is selected you should change to Mac App Store and identified developers to protect yourself.

Chrome should only be downloaded from Google's website

https://www.google.com/chrome/

any other link is suspect.

out of curiosity is there a phony chrome trying to make it's rounds on the net and if so do you recall where you got it?

clicking the installer icon to highlight and pressing CMD+i will (sometimes) show you the link you got it from.

Go to http://www.etresoft.com/etrecheck — download and run EtreCheck, copying the status report to paste here. It'll give us a glimpse of your system — maybe there's adware/malware on there causing these pop-ups. If so, we'll be able to advise you on how to get rid of it.

All OS X downloads are checked for safety when you try to open them. Mac OS X also checks for known instances of malware. If so, an alert message similar to yours appears: If you see "(file name) will damage your computer." You probably have a malware disguising itself as a Google browser look-alike. You should click Move to Trash. All Mac users should be extra careful when using software installers from untrusted sources. OS X improves download validation by providing file quarantine in applications that download files from the Internet.

Not sure why you are seeing that message but it certainly is not true.

Are you perhaps running any anti virus software? If so, remove it.