Well, one might wonder if the OED people in England and the NOAD people here really see eye-to-eye.

Whatever, there can be no doubt that when the NOAD people picked "carbon neutral," and referred to it as "a word," they knew perfectly well that they would be yanking the chains of a lot of conventional types.  I would naturally write it as Mihan suggests, "carbon-neutral."  But they are right about how compound English words work.  This new adjective has one well-defined meaning, and the presence of both the base adjective "neutral" and the nominal adverb "carbon" in front of it is essential.  Anyway, there are three ways to make such compounds in English: two words, two words with a hyphen, one word.  And different words are written differently at different stages of their evolution.  I do not exactly know if we currently write "man eater," "man-eater" or "maneater."  I would opt for the second, being a hyphenophile, but what do I know.  

These differences are not unimportant, I would say to the NOAD people.  A "blue bird" is not the same as a "bluebird."

And the more or less general rule, that compound adjectives should have a hyphen, is not just some purist's artificiality.  It truly helps us understand more quickly the syntax of the sentence in which it occurs.

But anyway, from their short list (or is that short-list?; or shortlist?), I would have voted for "fishapod."

Chickens deserve our true friendship! So do fish! So do other sentient beings! Let us learn to be kind.