Google added an experimental version of WebVR to Chrome as far back as version 56 earlier in the year, and there were a handful of sample web pages you could take a look at to test out the various features. Since then, more demos have been added and other uses have also been toyed with, including the interesting VR short-film, Tabel. In a recent AMA, the Chrome team said they were re-working WebVR, and it seems as though that job is done.
In a post on Google+, François Beaufort has announced that the first set of new WebVR features are there to try out in Chrome 61. If a site supports WebVR, you'll be able to view it in an immersive 3D experience. You'll also be able to seamlessly switch back to 2D if you navigate to a site that doesn't support that platform.
These capabilities are available right away. All you have to do is fire up Chrome on your Daydream-ready phone and head to any web page before placing it into the headset. Expect to hear more WebVR-related news in the near future, as François promised there would be more to come from his team. Unfortunately, I don't think this is compatible with Cardboard, but that might happen in the future.