I am guessing that this is a frost free unit? it sounds as though your unit is either very badly out of level which is unlikely or it has a blocked drain inside of the freezer behind the back plate, you will need to take out all drawers and unscrew the back plate then you should see a blockage in the drain hole (might just be iced up) do not ram anything sharp down the drain as you will cause damage, to test if it is clear after pour some warm (not boiling) water down the drain hole.
powerhousesteve, September 2010