Why are you worried it will die? A chicken run should be a great environment for growing a grassy crop, if the chickens are kept away for long enough of course. Chicken poop is high in nitrogen which suits leafy crops well. There are lots of other variables of course and none of us can comment on them without more info. There needs to be adequate moisture. It needs to be an appropriate grass seed for your climate. Inadequate drainage could be a problem. Presumably you haven't let the chickens onto the area to eat the seeds and no other birds have been having a go at it, and also you'll need to protect it until the grass is established. Little green shoots of grass would be heaven for chickens to graze on and would quickly be destroyed. Once it is established your chickens will make short work of it anyway likely.