So sorry to hear your chicken passed. I only found this thread just now. For future reference, I have found it best to try to handle sick birds at night when they have gone to roost, rather than try to chase them down and capture them during the day. They can't see well at night and it makes it much easier to examine them. Use as little light as possible to catch them so they don't try to fly. Also, try to take action as soon as their behavior looks "off" or different. Birds hide their illness as long as possible to protect them from predators, so when one looks or acts sick, often it is already very sick indeed. Again, I am sorry for your loss. Keep an eye on the rest of your flock and let us know if any others show symptoms.
Oh, almost forgot. If you double-bag your dead bird in plastic and refrigerate it (do not freeze), you can send it in to your state lab for a necropsy (animal equivalent of an autopsy) to learn why it died. I think
@casportpony has a list of labs by state.