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Hmm..maybe. Chidori requires not only agility and accuracy, but also a huge amount of chakra focused in one part of the body (hands). Neji certainly has accuracy, and he can focus his chakra in any part of his body, as shown in the 'retrieve Sasuke' arc. I'm not too sure if he has a huge reserve of chakra like Naruto or Sasuke, though. Also, Sasuke is naturally a lightning and fire type, so his Chidori is lightning-based. If Neji isn't a lightning type, then his Chidori might become a different element when his chakra is manifested--which is a pretty interesting thought. Imagine a stab of fire or water.

I don't know why people assume Neji to have any elemental nature at all (not to say that he doesn't have one, though), since there isn't really much evidence. Neji has always been predominantly 'Hyuuga'-based, which doesn't really have any inclination towards any element. I'm pretty sure we haven't seen what elemental moves coming from him yet (except I think there was a move that was called the "divine wind" or something like that, am I right?)

If I had to choose, he'd be wind-based. No particular reason why, but he just seems like that kind of person.

Without reading all that, Neji doesnt have a Lightening attributed chakra. The end. @.@

That doesn't mean he can't learn it. It just means it's harder for him. Besides, we don't know his affinities. He may be wind because of his abilities (I don't know, you try to find a hint). Other than that it's just pure speculation.

I think he can learn Chidori. Everyone can learn it. It's not just for Uchihas. =/

even if he could use it he probably could only use it once. neji is wind just think about how he makes the absolute barrier of his. its as it there was a wind to block people out.

I guess he could, yeah. But he most probably won't