The problem is the flapper door does not close, allowing moist air in and slowly freezes shut. Needs a new solenoid:
http://www.applianceblog.com/mainforums/ge-hotpoint/14017-fixed-ge-refigerator-ice-dispenser-wont-close.html
Will have to order one of these to see if this fix works!
EDIT: Oct 2012: I actually just disassmbled the entire ice chute from the inside of the freezer door. Just a couple screws and some plastic tab catches. There was a TON of ice under the area, and I was able to remove the ice block en masse , reassemble, and all is working great without a new mechanism. Sweet DIY!