you don't 'fight' the chicken (i can't believe i said this word), you just give them a code that, the chicken will give some story involving alice and that's pretty much it, at least that's what i know, the chicken will give nothing else after that.
the code can be found by talking to several NPC roaming in the world, or just open the txt file in your game folder. the last chicken demand a code inside a symmetrical house (the house have 2 doors), there's 2 note inside the house, that's the code you need to input