I had a chick with a wry neck in our first-ever chicken order. I wish I had culled it immediately.
Instead I succumbed to the pleas of the children to spare it. The longer it lives, the harder it is to cull, especially after the kids have named it. It survived about a year, but in the meantime I had to make special accommodations for it, to include keeping the water low to the floor, and the food had to be low also. As a result, the water for the chickens was fouled with droppings and litter most of the time, because it is impossible to keep a water fount that is sitting 2 inches off the floor clear of such things.