I’m pretty sure this came as a bundled app on the hardware but I have a Logitech Revue (Google TV) that I still use on my main TV. It’s a separate set-top box but it does have an Amazon Instant Video app on it and I have used it. The interface is still Amazon’s site essentially, but I’m able to stream video. I tried and i cannot stream Amazon Instant Video with the Chrome browser on Google TV.

Just thought I’d throw that in there. The app apparently exists, it just doesn’t exist on the Google Play store.