Amazon Prime Video support was promised at Apple's WWDC conference in June. Its addition makes Apple TV, along with Roku, one of the most flexible devices, especially now that Google has announced its plans to from Amazon's Fire TV platform. Google's own Chromecast does not support Amazon Video.
Amazon does not currently offer Apple TV hardware, but some suspect that may change now that Apple is supporting Amazon's video app. As of this morning, however, Apple TV is still not available on Amazon.
The Amazon Prime Video app can be found by searching in the Apple TV app store. We're downloading the app now and will update with hands-on impressions.