OK, I freely admit this is insane. But I couldn't resist trying the "Magic Loop" circular knitting technique to make the joining loops in a knitted chain.
I will say this: the flexible cord of the circular needles is very easy to pull through the knitted chain links as you move the links around ahead of your working stitches. But all in all, I think doing this with short, double-pointed needles is easiest of all.
It's possible that this insanity will extend to partnering with my fabulous friend Mary to make knitted versions of her beautiful chainmail creations.
Update December 17:
The chain felted up very nicely. It's about 6 feet long, and while it probably won't be very functional as a neck warmer, it looks pretty sharp as a decorative accessory.
In the end, I kept up with the Magic Loop experiment; it got easier as I went along.