I was testing a site on various other browsers today, and I needed the browser to present itself as FRESH to the web application, so with IE8 I used InPrivate blocking, and on Chrome I used Incognito mode. Both essentially works the same way, all cookies and browsing history information are discarded after the session, and no previous cookies are carried into the session.
There was no way this was a problem with Chrome or ASP.Net, but rather with Incognito mode itself. So I loaded up Fiddler and looked at the Requests coming out from Chrome Incognito mode. Then I realized that when in Incognito mode Chrome wasn't sending the UserAgent header that identified what browser was hitting the server.
Because of this ASP.Net could not determine if the client could properly process the script blocks, and thus decided to totally discard the delivery of the script chunk to the client. Of course, without said script chunk a lot of other things were affected.
After doing some poking around I found out that version 188.8.131.52 of Google Chrome seems to be the one afflicted with this issue. As this bug also stopped people from getting into Facebook and some Google sites, they quickly released an updated build 184.108.40.206 which fixes the problem. So update Chrome by going into Help->About->Update Now if you are having problems browsing some sites in incognito mode.
Though the automatic update system (which runs in the background even when Chome isn't running) SHOULD have updated the browser by now. But.. if you're having problems just update the browser and see what happens.