Unlike the iPhone and iPad, the Apple TV is seen as a side offering in Apple’s lineup and while it’s gained popularity in some circles, adoption is still nowhere as high as Apple’s iOS devices.

As a result, interest in jailbreaking Apple TV devices is pretty limited but the Apple TV 2nd generation, 4th generation and 4K are permanently jailbroken thanks to the BootROM exploits that affect them and because more developers showed interest in them. However, the Apple TV 3rd generation didn’t see any love and was left without a jailbreak partially because finding an entry point on the Apple TV firmware is more difficult than on iOS and because of the aforementioned lack of interest.
Now, that has finally changed as tihmstar, who’s behind jailbreaking iOS 8.4.1 and 9.3.5/6 with Siguza et al among other contributions, has released EtasonATV which is capable of jailbreaking Apple TV Firmware 7.4 (12H876; based on iOS 8.4.3) on the AppleTV3,2 with support for AppleTV3,1 units coming when someone steps in to help him with some minor things. Installing this jailbreak is a little different than traditional jailbreaks as it requires you to set a custom DNS address, add a profile and then open the Trailers app in order to jailbreak your device. After that, you can install a DEB file via SSH which gives you an untethered jailbreak (you needn’t apply it every reboot) for your device! For those asking why you should jailbreak an Apple TV, the main reason right now is the ability to install Kodi/XBMC (installation instructions).

You may learn more about EtasonATV by following this link which also contains installation instructions.