She may have gotten 'Got' my another animal sadly but I don't think she would run off to lay her egg and not return unless she found another flock to live with.
Was she laying eggs before she disappeared? Do you keep your chickens cooped over night? Do you have nest boxes in the coop? I don't think it's likely she disappeared to make a nest. Generally hens do that when they want to hatch chicks and don't want their eggs taken away. What breed was she? If you free range your birds you have to expect losses from ground predators as well as hawks. Chickens don't have much of a defense system . Basically all they can do fly off or hide in the brush.
I'm sorry to hear your girl disappeared. Since you mention "neighborhood" I assume you live in town...have you checked with neighbors? Maybe someone found her and took her in. I do hope you find her and get her back home to a secure coop/run.