I figured I'd post this to share, in case anyone else wants an inexpensive run ideas.
I took pallets and screwed them into each other. I also reinforced each seam by screwing a 1x8 into the ends of two pallets butted up against each other. I screwed the ends of the fence into my existing coop. I will be getting some t posts to reinforce the walls because I made it really simple and didn't dig post holes. I lined the inside with chicken wire. I did end up getting some 4' hog wire and stapling it to the top of the pallets so 2 feet of hog wire was sticking up (creating at 6' tall fence)-to keep the chickens from flying out/over the fence.
I just want to clarify that the only goal here is to keep chickens in. If trying to make it predator proof, you will need a higher wall lined with hardware cloth and some sort of dig proof barrier along the ground.

Edit:
I will be adding a hogwire roof because the chickens are able to escape. They figured out if they sit on top of the door that gives them access to the run, they can fly up to the hog wire and then out of the run completely.:barnie
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