Thanks for the alternate method for disabling updates in Chrome, Alex. I had gone through and done the Group Policy setup to prevent updates, but it appears that after I manually updated to the very last release of 43, that version started ignoring the "no update" policy and updated itself to 44...
As Tanya mentioned, Chrome 44 works with TestComplete 11 when the TC11 extension has been enabled (and chrome://flags/#enable-npapi is enabled).
Tried copying the Chrome/Application/<version> folder to the desktop, uninstalled Chrome, and then ran <version>/Installer/setup.exe, but it did not appear to do anything.