About the only negative consequences associated with chickens eating too many tomatoes are runny poops and dietary imbalance created by filling up on the tasty fruit instead of eating their poultry ration.
My flock adore tomatoes and would keep eating them as long as I cared to pick and toss them. It's ultimately up to us to dole them out in a reasonable amount or take steps to block the chickens from devouring the tomato plants.
By the way, leaves of the tomato plant are said to be poisonous. Chickens can eat a small amount and not suffer any ill effects, but you need to watch that an individual with minimal instincts for self preservation doesn't stand at a plant and eat it to the ground. I would suspect you might see a chicken suffer from that particular culinary indiscretion.
