I am deeply disappointed to know that I can't use Skype on my new XBOX 360.
Tough it is not directly skype's problem, there must be a solution and MS and skype should do something together.
Xbox One will feature a Skype app this November. More information here: http://www.xbox.com/en-US/xbox-one/entertainment
A Skype application for the Xbox 360 has not been announced yet.
I really hope we do get a Skype for XBox 360 app. We bought ours right before the XBox One was announced and I don't want to feel like our new machine is already obsolete!