Chrome showing the site's security certificate is not trusted for GitHub
An old certificate expired on July 26h, 2014. Many users had it stored in their keychains, causing the errors you saw. Here is a detailed solution:

Based on https://www.yesthatallen.com/fixing-an-old-digicert-issue/

Instructions for clearing expired DigiCert SSL certificate on OSX


Launch Keychain Access via Spotlight

⌘-Space
Type "Keychain Access"
Hit return

Ensure expired certificates are shown; enable "Show Expired Certificates" in the "View" menu.
Search for "Digicert".
Right-click the certificate with a red X and select "Delete DigiCert High Assurance EV Root CA"
The certificate may not look removed until Keychain Access is restarted
Restart your browsers
You should once again be able to access the affected sites.
Run Software update if problems persist, to make sure the latest root certificates from Apple are in place.