Update - One huge design flaw we discovered is that water collects on the flat roof and it has nowhere to go. During an overnight storm, it collapsed the run. Now we've had to find new poles and reconstruct the roof. My advice is to buy a run one with a peaked or rounded roof. 

This does the trick, but the chicken wire is cut in odd sections and had to be "sewn" together to cover the width of the run. Also, the chicken wire is not very sturdy and we'll need to buy additional (higher quality) wire to provide the necessary protection.