"A chicken is a bird."
Translation:Курица - это птица.
Since the Russian language dropped the verb 'to be' in most cases, sentences like «X is Y» became easily confusable with appositions «X-Y». So, «Курица — птица» 'A chicken [is] a bird' can be confused with «курица-птица» 'a chicken bird, a bird of a chicken'.
If you think this is not someone would say, you should check Russian folklore: it has lots of things like «Сирин-птица» (a bird Sirin). Well, you don't find many traditional poetic texts about chicken, alas! But still, the construction is ambiguous.
So, to distinguish these two usages, Russian has introduced a pronoun 'э́то' in the construction «X is Y»: «Ку́рица — это пти́ца» (literally "Hen, it [is a] bird"). It might seem redundant from the English point of view, but in Russian э́то serves a purpose. And while you still can say «Ку́рица — пти́ца», it's not what Russian speaker would usually say, it would sound unnatural.
I am a native speaker of Russian, have lived in Russia all my life, but to me «Курица — птица» doesn't sound unnatural at all as a sentence (in fact, I've chosen it as an answer). As long as you say it with a proper intonation, it will not sound as an apposition, so это IS redundant after all. It's true that это is widely used in giving definitions, but it doesn't make it a mandatory thing.
«Курица не птица» doesn’t literally mean what it says. It is part of the old Soviet saying «курица не птица, Болгария не заграница», which means “just like a chicken is not good enough to be considered a real bird (it can’t fly far and high), Bulgaria is not sufficiently different from the Soviet Union to be considered a foreign country”.
«Курица — это не что иное, как птица». The register of this sentence, though, is not as low as that of your sentence with “ain’t nothing”. The Russian sentence is rather formal. In an informal conversation one would say, «Конечно, курица — птица. Если не птица, то кто же?» (Of course, a chicken is a bird. If not, what is it?).