I used it with Chrome yesterday just fine. Maybe your Chrome doesn't have Silverlight correctly installed, for the on-demand video? For the video that's what really matters, the browser is just a container at that point regardless of which browser it is.
Huh, Chrome works for me too, and that's a fairly new development, like the last month or two. Officially, Netflix streaming in a browser still only supports Firefox, Safari, and IE.
This seems really odd to me because I've been using Netflix with Chrome for at least a year now, and I didn't do anything special, just installed silverlight and it worked.