There should have been a micro-USB cable and USB power adapter in the box. The G70 receiver can be powered either by a 9V DC connection or the micro-USB jack. I would recommend getting a 9V power supply for long term use, but the USB power supply that comes with it will work out of the box.
Somebody at the factory screwed up and left it out of the box, or someone at the retailer stole the adapter and cable out of your box, because the G70 system comes with the adapter and a USB to micro USB cable. It's in the manual and everything...
I know it's about a year too late, but I would have contacted Line 6 about sending me a USB power adapter.