I got it back together because I suddenly remembered how I had done it before. I glued 1 jaw with C/A glue to a cutting mat. I inserted the spring with tweezers into the hole of jaw 1. I took jaw 2 and inserted the other end of the spring into jaw 2. I positioned jaw 2 and glued it to the cutting mat. I took jaw three and placed the third spring in place and also the other end of the first spring. Then I glued jaw 3 into place. I could slip the chuck casing over the three jaws. The jaws slid into place with the springs getting compressed. I twisted the case until the jaws were released from the cutting mat. I am now soaking the chuck in acetone to remove the residual C/A glue.
I was more interested in getting this thing back together than in taking decent pictures. Here are crappy photos! I was fidgeting with these parts like a crack addict with Parkinson's.
Step 1
Step 2 and 3
Back in!