Rod actually scored first, a couple of days ago. And now the rest of you have zeroed in on it. It is, indeed, a base Pzkw IV (H) chassis with a one-off experimental hydrostatic transmission. Putatively built to a request from the SS, and found at the factory in Augsburg, Germany, by a US Weapons Technical Intelligence Team, and brought back to the US, to Aberdeen Proving Grounds - more accurately known amongst the military vehicle grognards as "Aberdeen Rusting Grounds." The Ordnance Corps museum, while home to a fine small arms collection, was a wholly inadequate conservator of the historic armored vehicles and artillery entrusted to their care. This is a very American problem, where the best-preserved, and running vehicles, are mostly in private hands, such as
the late Jacques Littlefield's collection in California, or the
American Wartime Museum (aka "Tank Farm") in Virginia. Compare to
Bovington,
Saumur,
Muenster Lager and
Kubinka (where at least they've got most of their stuff under cover) and
Latrun, in Israel, where the weather is conducive to open storage. By contrast to Aberdeen, where it rained about 4 inches the three days I was there... if you want more details on the tank, click
here,
here, and
here. I'll have a rant about Aberdeen's current condition later this week. In their defense, they're moving the Ordnance Museum from Aberdeen to Fort Lee, VA, where the Ordnance School was moved as a part of the 2005 Base Realignment and Closure Commission recommendations.

You can see from the broader perspective of this picture that there are empty slots in the field where the static display vehicles were. But let's get back to this unique, one-of-a-kind tank that just sits there rotting in the weather...

It's looks like a standard Pzkw IV (H) except there are two sprockets and the rear looks odd - oh, and no provision for side skirts - the turret has schuerzen, but there are no brackets and mounts for them on the hull.

The plaque that is on the ground in front of the vehicle says it never saw combat - though it was apparently hurriedly positioned to defend the factory - however, someone dinged it at some point, here on the muzzle brake.
Apparently when the "new" museum was built (I believe with private funds since the Army no longer gave a rat's behind about historic artifacts under Carter's reign of incompetence) it was necessary to leave the big stuff outside in the weather. That was also about the time that they went thru and deactivated all the small arms by welding them up etc as some sort of loony "safety or security" precuation.
Moving stuff to Lee, if it's going to be outside, actually worse than leaving it at Aberdeen. Far more humid during a greater part of the year. I'd hate to see that stuff at Stewart 12 years later.