Google's help site identifies three causes for the problem: a conflict with a security app or other software on your system, a browser cache in need of clearing, and a temporary outage of the Gmail servers.
The About Google Chrome window shows the current version and whether an update is available for download. Since Chrome updates automatically, this should be a no-brainer, but to make sure you have the latest Chrome version, click the wrench icon and choose About Google Chrome to open a window listing the version number and indicating whether an update is available. The Google Help page for Gmail-loading problems suggests you make sure your browser is up-to-date. This temporary technique worked for me as well, but another proposed solution-using an encrypted connection (HTTPS) to open Gmail-didn't get my inbox to appear. If clearing Chrome's cache doesn't get Gmail loading again, the simplest alternative workaround is to press Ctrl-Shift-N to open an incognito window prior to signing into your Gmail inbox.
One possible fix for Gmail's inability to open in Chrome is to clear the browser's cache via the 'Clear browsing data' dialog box.