The third guy's full of it.
Either the first guy is a liar or isn't. Either way, he has to say he isn't. If he tells the truth, he must say he is a truth-teller, and if he is a liar, he cannot say so, so he will say he's a truth-teller. Thus when the second guy reports that the first one said he was a truth-teller, this is true. So the second guy isn't lying. Therefore the third one is.