Mine have a long run for when we're at work and free range every day. I have covered the top and sides of the run with a combo of shower curtains and clear tarp held on by bungee cords. I think a gazebo would blow away.
Have a look on the Omlet forums and you will see photos of customised runs. Good luck to our poor girls!
We are not chicken keepers but had the idea of leaving the gazebo up on the patio - bad idea! rain weighs down the top and if you dont go out and push it off everyday the weight buckles the struts = no gazebo