It's "das Huhn" (neuter), so your example doesn't work. When the forms are identical (say, for "die Birne"), you have to guess from the context which one is meant. Also, while there is no required word order in German, there is a "neutral" order (subject first), and whenever you deviate from that order parts of the sentence get emphasized. So if the sentence ambigous, one would probably try the "neutral" order first, unless there are other cues (e.g. stress when talking) that some part of the sentence is emphasized.

I get what you're trying to imply :D But Huhn is neuter: das. In akkusativ neuter is also "das", so its actually: "Die Frau isst das Huhn" = The woman eats the chicken and "Das Huhn isst die Frau" = The woman eats the chicken/The chicken is eaten by the woman versus "Das Huhn isst die Frau" and "Die Frau isst das Huhn".¨ And allthough this mistake has been corected, you might still notice that the sentences has been repeated, but their meaning differs. And although this is what you're wondering about, it is as it is, unchangeable. In this kind of sentence, it is though understandable that the woman eats the chicken no matter how you say it, and no one would probably understand it as if the woman was eaten by the chicken. But no doubt that it CAN be understood as "the chicken eats the woman". So normally you wouldn't just say "The chicken ate the woman" in German, because everybody would understand it as if the woman hat eaten the chicken. Thats why you have to specify: "I saw a chicken which ate the woman" or something like that. I must though confess that my german gramma isn't the best, and since I'm not quite fluent I may be mistaken. But truly I understand your confusement, but to me I would never doubt that the woman ate the chicken and not vice versa. If I still doubted the statement I would ask you into it, and you would specify :P