Well, after studying the fiber, I have determined that this is NOT wool after all. Oh well.
I cut off a small portion and took it apart into the 3 separate plies. Then, I took one ply in my fingers and untwisted it. It was easy to see that it was not wool, because it had no staple length at all. It has very fine fibers that are tightly spun - not a single hair in there - and it shines like nylon. There is a ply that is darker in color, but it appears to be the same content - just dyed a dark blue.
Then, I decided to try the burn test. http://www.fabriclink.com/Burntest.html
The yarn strand burned VERY quickly, and completely melted away. So, it's definitely a manmade fiber. Probably acrylic, nylon, or polyester.
But, I do have a LOT of it, and it looks good. I think it will still make a nice sweater. I'm thinking that it was probably a sweater in a former life. An enterprising person probably unraveled the sweater and put the yarn in hanks.
So much for the mystery!