On the other hand, your chickens may quite enjoy bits and bobs like chopped up beet tops, pea leaves, or carrot greens. They'll probably also enjoy your pumpkin seeds---that is, if you don't toast them up for yourself. And they always seem to enjoy the leftover watermelon rinds. If your tomato has been chewed on by a caterpillar, your chickens won't care! However, you won't want to offer them anything rotten/moldy. Stick to giving them produce that doesn't meet your standards of beauty, or that has a "fresh" wound, not a festering one.
Proceed very carefully, though. We suggest putting most garden waste in your compost pile unless you know for sure that what you have is not toxic to chickens. Additionally, as most veggies are fairly low in protein, offer these "garden treats" sparingly. Most of their diet should come from their nutritionally balanced feed.