First: from some of your comments, it appears you're not planning to actually use your web application in a browser. If I'm wrong, see below. If I'm right, then you're perfectly fine to write whatever UI you want using whatever technology you want and connect to your web application via that UI program. There are issues you'll have to deal with: what platform, what technology, etc. But you'll have no problems connecting to your web application using such a UI; just follow the HTTP protocols in your socket programming or use a framework that does it for you.
That said, if you're planning to do 3d in-browser, you should look into the Google O3D API. It's a browser plugin, but it should give you everything you need to do 3d in-browser using the GPU rather than software rendering like Flash and Silverlight do.
If you're not willing to use a browser plugin and you're not trying to do your own UI program, then your only other option is to use Canvas and Chrome Experiments as @Kitsune has suggested.