The developer tools (F12) gave me the error: ERR_SPDY_PROTOCOL_ERROR. I googled a bit and found many articles, but none gave me the solution. One did give a part of the clue: a post on the Cloudflare forum talked about a discrepancy between the length of the content and the value of the content-length header. What could cause that? I thought about a compression issue and checked the settings of my IIS server. Both the static and dynamic content compression settings were enabled, something I do by default when I create a site on IIS. Apparently, when HTTP2/SPDY is enabled, Chrome does an additional check on the content length. A possible solution was to disable SPDY on Cloudflare, something that can only be done through the API. I preferred to disable compression at the source, and presto, the site was available again on Chrome...
To disable compression you can do it through the web.config file of the site:
inside the webServer node or use the GUI that will update the file for you:<urlCompression doStaticCompression="false" doDynamicCompression="false" />
And click "Apply" in the "Actions" pane on the right side.
Simple solution to this problem, I just needed to find out about it ;-)
Hope this helps anyone.