Amazon is rolling out a software update for its family of Fire TV set-top boxes and sticks, which allows users to control them via an Alexa-enabled device, such as an Echo or Echo Dot. The version number will either be Fire OS 184.108.40.206 or 220.127.116.11, depending on which device you're using.
According to the changelog, you can use it for playback commands such as play, pause, rewind, etc., but you can also use it to open apps and search Amazon's library of movies and TV shows. You'll first need to pair the two devices through the Alexa app. There's a link in the changelog that should take you somewhere that shows you how to do that, but it just opens Amazon's general help section.
If you've got a Fire TV with a Voice Remote, then the device itself already has Alexa; however, you need to press the button on the remote to activate it. With this new feature, it's completely hands-free.
The update is available for all Fire TV devices, which include the first-generation Fire TV Stick.