I have a chain with 10 bones. I want one end of the chain attached to one hand and the other end attached to the other hand. Is there a way to do that so when I move either arm the chain moves with it?

Unfortunately, it cannot be achieved. iClone does not have IK for props.
So chain rig would not follow hands even if you managed to attach it to both hands.
Animating manually would be a nightmare (depends on what you need to do with it).

The only other way to somewhat simulate the action, is to use rigid physics based chain.

I could not come up with any better idea for the chain action using both hand other than this in 4sec. clip:



Chain physics is quite fragile and if you never dealt with it, there is a lot to learn.
You may download a Demo project and study it: https://drive.google.com/file/d/18pGjDKt8sE709teIx9wJcUp3ssh2JBqB/view?usp=sharing

Notes: Rigid Physics bakes animation on the fly. I disabled it in Project so that the action can be visualized in view-port real-time.
When you are ready to animate, you'd need to enable rigid physics, animate hands and play back in ByFrame mode.
Sometimes you'd need to start and stop the "Play" 2 times to have the physics properly initialize.
Watch out for characters collition shapes. Chain would be actively interacting when it comes in contact with them.

Thanks for your help. (o: