Original WWII German fur vest, typically worn as a liner underneath coats and parkas. This one is a size 2 which fits approximately 38-40 chests. Although unissued, the skin and fur are 80 years old and a few stitches are coming loose here and there on the binding. Therefore, if one is a reenactor and is contemplating wearing this, chances are it wouldn't hold up very well.
As for markings, there are a few letters and numbers, hand-written in colored pencil scattered about which are from the factory that made it.

Buttons are the 20mm pressed paper type typically found on the white side of Waffen SS parkas. Does that mean this is an SS vest? Well, no window licker has smacked "SS BW" stamps all over it yet so it can be whatever one wishes.

One only.