After I tossed her back in, I took a closer look at the temporary fence, which is the plastic orange netting used for catching snowdrifts (we excel at drifting on the property, which is presumably why the previous owners had the stuff). Down at the bottom was a hen-sized rip in the plastic strips. Aha.
Now I'm not saying that they actively ripped the fencing. It could have happened in the wind because we hold the base tight against the ground with cinder blocks and bricks. But it was suspiciously just the right size for a hen. No, the interesting part is that their pea-brains don't seem to know where the hole is. They were just congregating along the fence to see me and Pop! out one comes. So has Walkabout been getting out on purpose or by accident? And clearly, once out, finding the hole again was beyond any power of chicken reasoning.
I tied up the hole with some string. Let's see if they can undo a square knot. They untie shoe laces pretty well.