do we need a roof?

I have also posted this in the fox alert thread, but unsure where to put it.

Hi, I am new to the forum and have a specific question about old mr foxy!  Sorry I haven't read through all the posts on this thread as there are rather a lot!

We have the hen house and are now clearing the overgrown area in our graden to accomodate the chooks.  The area is raised from the main garden, but still a fair size.  It is amongst a couple of large trees, so my question is do we put a roof on the run?  We live on the edge of wilderness, so foxy will definatley come prowling, but would an open topped run so the chooks can get up into the trees, if he did manage to get in, be better than an enclosed one?   

Thanks

Or electric fencing deters foxes and then you would not need a roof.

I quite like the idea of them having access to the trees and for escape. Living under trees is their natural environment.