I don't think it will for a long time if ever. TWC seems to be pushing mostly the Roku box solution. It been a long time and nothing ever seems to be done.
At this time, no information or plans have been made available as to if or when that would be available for the Apple TV platform.
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THERE WILL BE AN APPLE TV APP FOR TWC SUBSCRIBERS VERY SOON!!!!!!!!!I know this is a relatively old thread but, I have good news for everyone who hasn't been paying attention to the fact TWC was aquired by Charter. Charter is developing an app for the Apple TV and will be available in the next few months according to them. Obviously if TWC was developing an app they are not anymore so this is the answer to our hopes.