You might want to read the label of your fertilizer and see what it says. The chickens may or may not eat it. You won't know until you put it down.
I've heard that alfalfa makes a great lawn fertilizer. You can buy it in 50 lb. bags from the feed store and use a lawn spreader to put it on the grass. It's cheap, high in nitrogen and breaks down fast after it rains. And if the chickens eat it you don't have to worry.
You could also look into all natural or organic fertilizers that won't pose a risk to birds.