Chrome showing the site's security certificate is not trusted for GitHub

I had this same problem. Open Keychain Access in Applications>Utilities. Make sure the selected keychain (top left) is login and the category (middle to bottom left) is certificates. Right click on any certificates labeled DigiCert and delete them. That should fix the problem.

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.