Happy ending! The neighbor finally called (I had left my name and number on a piece of paper under his doorstep). The hen is doing well and will get her wings clipped this weekend. I'm glad I didn't go into his yard though because I'd rather be safe (and I was with my daughters all day) than risk my health, despite how awful I felt for the chicken. I hadn't yet clipped the wings of the two youngest birds we inherited, so this is a good reminder. All of our chickens are curious and good flyers, so it really helps to clip their wings.
Thanks for all your good words today! I really appreciate it.