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Maybe you could look into native client for straight chrome. I know it is possible to write games in C++ and have it compiled into the native client. I think it is extremely locked down so no direct access to the users disk but maybe it will give you what you want which seems to be C++ access to a webpage.
It might be possible to create your own plugin (so something like flash) that is displayed in a particular part of the webpage, if you are using old internet explorer you can even embed an ActiveX control directly in the page! However these methods are not popular and everyone is trying to move away from them towards html5 instead.