Chicken died....should I be worried about the others?

The missing breast feathers could be down to the bird molting or even going broody.  Was the bird showing any signs of illness before it died?  Same for your neighbours birds?

I would start by checking the coop for red mites as they can die due to loss of blood.  Check for lice on her and your other birds.  Have they been wormed with flubenvet recently?  Could it just be down to old age?

Apart from that you would need to take the bird for an autopsy straight away to have tests done to determine the cause.