I do not believe that chidori can pierce kaiten. This is based on the properties of both techniques and how they work against chidori managing to breach kaiten.
Let us first consider the properties of chidori. It is a technique which relies on linear, extremely high-speed approach to pierce targets at zero-range. A secondary effect of the technique is local paralysis where the target is struck, but considering the fact that if the attacks lands the target would be dead anyway, this is usually not mentioned.
The kaiten, on the other hand, is a technique which CONSTANTLY projects a very high-speed, rotating dome of chakra from the users body. This is all it does, but its strength also lies in its simplicity.
If the chidori were to be used against an already active kaiten, the chidori would fail to even reach the target because 1) despite the chidori users hand being encased in chakra, it is still just a hand underneath, and would therefore be deflected in the direction of the spin, throwing throwing the user away. Also 2) even IF the user managed to get their chidori encased hand within the chakra dome, as stated above, the dome is projected at least an entire body's width from the user, so they would not be reached. Seeing as the attack needs to connect for the electricity to paralyze the foe, the chidori is completely useless against the kaiten.
This is a strict comparison of chidori vs kaiten, and does NOT take into consideration the techniques derived from chidori (nagashi, eisou) because they are different techniques, and this is also not a comparison between Sasuke and Neji/Hiashi.
What do you think?