So yes, you'll have to charge it through your computer with the supplied USB cable. The first accessory I got for my player (I don't have a Zune) was an AC adapter. The second was a case.
My first mp3 player I ever bought was Creative Nomad Zen Xtra 30GB in 2003. You have the supplied AC wall charger that comes with the mp3 player to charge the battery. However, what I noticed on the included accessory section of all online stores, a battery charger is not listed. So even though this may be a very stupid question my question would be; how do you charge the battery on the Microsoft Zune? Do you charge the battery with the Supplied USB cable on a computer? Pleas help. Thanks

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