According to Google this can be accomplished by visiting "chrome-devtools://devtools/devtools.html" in Chrome but now visiting that page in the stable version of Chrome (or Canary), just shows a 99% stripped version of the inspector.
To reiterate my "title" this is in reference to "inspecting" the inspector. Not just inspecting a normal webpage.
And while I don't think it's necessary to know to resolve the issue, I"m inspecting the inspector so I can style it as discussed by Paul Irish and here: https://darcyclarke.me/articles/development/skin-your-chrome-inspector/
Follow these easy steps!
Press Command+Option+i (Ctrl+Shift+i on Windows) to open DevTools.
Make sure that the developer tools are undocked into a new window. You may have to undock from the menu:
Press Command+Option+i again on this new window.
That will open the DevTools on the DevTools.
A little beyond the scope of your question, but still valid in understanding why you're experiencing your problem can be found by understanding how Chrome Developer Tools: Remote Debugging works.