Good question!

In the US I find this spelled two different ways, chené, and chainé.

It's a French word (I think) and ballet uses the same term (both spellings!).

The most common usage is chainé. When I look this up in a French dictionary, I find only chaîne, meaning chain. When I look up chené, I find only chêne, meaning oak. Some meanings of chaîne are suitable to the movement envolved, and chêne seems to be way off-base, but this is really only a guess on my part. I found no listing for chanait.

You may also find some difference in pronunciation depending on where you are located. The English pronunciation of French words is usually different from the US pronunciation of the same French word. In the US both of the spellings listed above are pronounced the same way, sheh-nay'.

I suspect chainé is correct and chené is in error.