This must be happening at night, yes? Otherwise I would think the the chickens would be feasting on the roaches. I don't know? Glue traps might catch some of the creepy crawlies. Just make sure you collect them before they get stuck to your chickens!
Try securing the feed better. Other option would be to only put the feed out during the day in small bits, check it once and a while, and find out where the roaches are nesting. Killing them one by one won't help (stomping on them with your foot, etc). If you really needed to, you could move your chickens out of the coop and into a secure place inside a garage/basement (only if you have 10 or less). Then control the pests from there with chemicals after stripping everything down.