Unfortunately at this time, we do not have a native app. This is something that I'd really like as well but will require a lot of resources to make happen. It's an idea being tossed around right now.

In the meantime, we do have a list of our 3rd party apps here. Some of them might do enough for you, but they do not replicate the TMDb experience nor are they officially sanctioned by us.

Oh, and P.S. you can always use the "Add to Home screen" option in Chrome to link a dedicated window straight from your homescreen.