Hello wine, ripe tomatoes are fine for chickens. The rest of the plant is not good for them - if my chickens are foraging around in the garden they will trample the tomato plants
but not eat them.
Did you know tomatoes, potatoes and tobacco are variations on the same plant? In theory you could graft a potato root, a tomato top and tobacco leaves!
All three of the plants contain similar chemicals which are toxic in high doses. So green potatoes, leaves of tomatoes, and smoking are all bad for your chickens. Cooked potatoes ad ripe tomatoes are fine.