Thank you SO much for all of the support and great advice. I summoned my courage yesterday and took the long walk to the neighbor's house, 3-year-old twins in tow. The house is a short distance from my backyard to theirs, but much farther if I go around the proper way down the driveway. I figured that it's a lot harder for someone to get irate and yell and scream if you have toddlers with you.
I was very nervous because I really don't know these people at all and I had no idea how they might react.
Excellent - no, stupendous - news! First of all, the husband had had a couple of days to calm down. The wife was very nice. Best of all...
THE CHICKEN IS NOT DEAD!!!
Here is what appears to have happened: They have 5 or 6 chickens and a good-sized coop inside a large chicken-wire fence. They do regularly let the chickens out to roam around the yard though. Apparently my Old Man decided to take a walk around the neighborhood, saw the chickens and got very excited. I think the neighbor heard the chickens going mad and ran out there to find my dog, one chicken lying in the grass, and no others to be seen. He went to my guy to look at his collar and find out to whom he belongs. My dog slipped his head right out of the collar and then decided to play with the neighbor's dog (who, btw was not in any sort of fenced enclosure).
The neighbor told me that when he went to gather the dead chicken, He started to lift it up with the pitchfork and the dear thing startled awake. They told me that it had even laid an egg the next morning. Apparently it had been frightened nearly to death but not mauled by my dog. I can not tell you how relieved I was. I nearly broke down in tears!
The man has a large property with lots and lots of trees. He has a sawmill in his yard and had recently cut down a number of trees that had come down during a recent ice storm. He showed me the stack and said it was drying out and that we could use some to build our own coop. I assured them both that we have *always* been good neighbors, that we are taking steps to ensure that Apollo doesn't get out again and that I would love some advice when I'm ready to get my own chickens.
All and all, very good news.