GAH! I hate thread breaks, they slow down the whole process.
TIP: Ring Closing Thread Breaks
With a break like this it is really important to backup your work to ensure the most beautiful and strong repair possible. In a piece like the one pictured above, I recommend using a scissor to cut the ring in half before the joining picot (but as close to this picot as possible). You should then be able to pull apart the stitches easily enough after doing this to get back to the base of the previous chain. This will look something like the picture below.
DO NOT try and tie your shuttle thread back on to the broken thread. It is nearly impossible to work over knots going forward with the piece. In addition, knotting will cause a lumpy section in your work which will detract from its beauty. Instead, trim your shuttle thread at the breakage point to make sure you have a clean, non-frayed end. Wrap the shuttle thread around your hand in the normal way to prepare to make a ring. Simply pull the broken thread through the middle of the turned stitches as you continue with your ring. I would continue doing this for at least 3-5 stitches to ensure the strength and durability of the join. Once, finished with those few stitches, trim the broken thread and complete your ring. When reversing work to complete the next chain, you will apply the same technique to the new thread's tail. As you will see below, using this technique will result in a perfectly lovely fix!
Well, despite the several thread breaks, things all came together finally last night. Here is the final piece prior to being added to the headband: