Update: The HBO Now iOS app has been updated to version 1.2.0 with Chromecast support.
HBO's streaming service HBO Now is launching exclusively to Apple devices in April. This means you will need the HBO Now iOS app or Apple TV to sign up for an account, but once you have a subscription you will be able to access HBO Now through HBONOW.com. HBO subscribers should then be able to stream content using their Mac or PC and Chromecast.
The HBO and Apple deal is also a timed exclusive. This means around July HBO will be able to bring HBO Now to other platforms such as Roku, PlayStation and so on.
More details will be known once the service is officially launched.