Found the culprit.
The neighbor's black kitty, who looks for all the world, like mine, has just been spotted in my backyard. Chickens were everywhere. No dead ones, but every chicken was somewhere I have never seen them before. Several on the deck, two stories up. two around the corner, on the handrail, where you can't see them from the backyard. The leader, wandering the side yard. I went around the side and saw two up, on the side of the house. I held up my hands and the black bantam flew right past them, into my hair. She climbed all over my shoulders and chest.
Those claws work
great on clothes! No pain, like you'd get if a cat climbed you. She just walked all over me, like I was made of Velcro. Like the mythical, rare and elusive furry Mountain Chicken, seen only in blurry photos.
The barred one stayed up there but looked like she wanted to come down. The HCIC (Head Chicken In Charge), climbed to the top of the deck and crowed (she might be a he). The barred one responded by walking to the HCIC.
I have a live trap, that might work well for the cat. Then it and I will need to have a conversation that may involve the business end of a garden hose. I think if the cat goes home a little wet (or unrecognizably soaked), it may decide to stay home and that chicken tastes better dried, in cat-food form, rather than, on the hoof.
Some of the chickens clearly enjoyed toying with the cat, but others looked fearful. The one RI that went out front, followed me to the gate on the other side of the house and walked through. That was cute. They do seem to recognize me.
I talk to them with "Psh psh psh" noises, that imitate the noises they make. But then I'm also one of those idiots who acts like they lost their mind, around kittens....