NO. You will have to purchase the drive and be responsible for replacement should it crash, but no fees from Verizon. You also must have a 7216 or 7232 Motorola DVR or the Cisco DVR - the old 6416 Motorola does not have the expansion port.
Note: Someone should tell the Verizon Customer Service People that there is no fee associated with adding an external drive to a DVR. I called 3 times.... There final response was " We don't know".
