If you can't find a short in fused and/or non fused branch circuits, the short is inside the alternator. Seen this a quite a few times before in all types, not just Chrysler.
I recently had the same problem on a newer VW. The alternator was dragging down the battery and if it sat a couple of days it would be dead. I found the problem with an ammeter in series with the battery. Once I disconnected the alternator wire the ammeter went to zero. Of course being a VW it was a real pain to work on too.