Present tense is accepted too. "We do not pay for the chicken". Both use "pagamos". =)
Why isn't "We don't pay for chicken" acceptable? It has to be "the chicken"?
Because in this case it is using "pela" which is pretty much "por + a" (for + the). So the the is necessary here. =]
Wouldn't the present tense "we don't pay for the chicken" be correct as well?
Yes. It would be less common, but it would still be correct. I can imagine your sentence being uttered as a part of a bigger context:
"Let's do it this way: We don't pay for the chicken, and you don't pay for the pigs. OK?"
"Vamos fazer assim: nós não pagamos pela galinha, e você não paga pelos porcos. Tá bom?"
I think that's right, technically, but in English we often just use "chicken" to refer to hens, and we only use "hen" when we need to be specific. So, if anything, "hen" should simply be added to the accepted translations, along with "chicken"
As far as I understood, "galinha" literally means chicken whereas "frango" refers to cooked, edible chicken. Is that about right?