I started out with a chain that was so stiff that it was almost like a stick that was limp in a couple of places. There is no way that it would whip like a chain if you wiggled it back and forth. It looked like trash. I soaked it for a while and it didn't help a damn thing. Then I grabbed some pliers and tried to loosed up the chain links by moving them back and forth. It was really dirty.
Here is what I started with on the vice. The vice made a great surface to drive the chain with the punch.
But then I thought, "what is a chain?". It's a couple of plates held together by a couple of pins with rollers to keep the plates held apart wide enough for the matching sprocket. There is an inner and outer link from one link to the next. These are held to a desired width with pins that are pressed together. Well if the inner link is binding with the outer link then you can free them so that they don't bind. I did this with a simple punch and hammer. If you punch the inner link down away from the outer link then they will pivot freely. It's hard to explain but just look at the pictures below.
This is obviously at the very beginning while the chain was still pretty rusty but oiled down. Now I just tapped each inner link inbetween the outer ones and this made them separate just enough so that they wouldn't bind and also oil could get inbetween these links much better. The rollers keep the inner link from compressing too far so the sprocket will easily still fit.