This is what I did a few times on many sizes of chain including very small link chain. I first measured out my chain for lengths and turns depending how it would be attached to the ship. I then took a cardboard box and mounted the chain with long straight pins on the 'side' of the box so I could get all the way around the chain and hold it in the configuration I needed. Keep the chain slack between the pins so that while brushing on the paint, the links move around some. That way you get in between where the links loop with each other. I then thinned down some flat black paint so it would not be so thick and painted the chain. It was dry enough after about an hour and a half to handle. I then removed it from the box and carefully touched up where the pins had made contact with the chain. The chain was still a little stiff from the paint but not near as stiff as when you use paint straight from the bottle. After letting it sit for a couple of hours more, it's ready to place on your ship with a minimum of repositioning. To mount it, I used Testor's Clear Parts Cement since it doesn't attack the plastic or the paint. I run a fine line where the chain will be and then lay the chain in place. I think my ships looked great but it took me a couple of practice runs to get the paint thickness right.
If you have an airbrush it's even easier. Hold the chain straight up and down and as you spray constantly raise and lower the chain onto a hard surface until it is completely covered. After your done spraying, do it 2 or 3 more times and your done. I did this on my last ship and it was the best. There was no stiffness and sticking of links together. The chain looked like it was bought that way.
Hope this helps.
Dale