This gun is the M4A3 Grease Gun. It is good at short range, and for clearing bunkers. A fully automatic, blowback operated SMG, which is cheaper and easier to make then the Thompson SMG.
The following additional information is courtesy of Bob Caulkins:
"I carried a grease gun in Vietnam while I served with the First Marine Division (66-68). There are several neat things about the gun that don't appear in the description, and I'd like to tell you about them. The gun had a built-in oiler in the base of the grip. After turning the gun over, the knob seen in the illustration is unscrewed revealing an oil reservoir and an oil applicator. The wire stock was a masterpiece of American ingenuity. It was a wrench for removing the barrel, the barrel had two grooves machined into it into which the wire stock was placed and then turned to loosen the barrel. One of the stock rods was threaded at the forward end to take a bore brush and drilled out to take a cleaning patch, and finally, there was a small "L" shaped piece of steel welded to the butt of the stock, as seen in the illustration, that functioned as a magazine loader. Trying to thumb load 30 rounds into the mag was a chore. This twenty-eight dollar, or so, piece of stamped, welded and machined metal was a beauty, on the several occasions when I needed it, it never failed me. "