I am currently analysing my page connections and I want to block some tracking scripts and other external URL calls in my network monitor inside Chrome\'s developer tools.
As pointed out by @calavera.info, @iman.Bahrampour, and @Asim K T this feature is now available in Chrome 59. You can select a URL or domain to block in the Network panel. See this release note and these Screenshots where the StackOverflow logo has been blocked from this page. @iman.Bahrampour also shares two extensions below that will also do this ("HTTP Request Blocker" and "Request Blocker").
This is now achievable in Chrome 59 developer tools by blocking respective requests: https://developers.google.com/web/updates/2017/04/devtools-release-notes#block-requests. With this approach it is somehow difficult to turn off all the stylesheets, but it's easier to turn off just the most annoying ones.