I’m a mom with 2 kids ages 5 & 8. I just bought a chicken coop and am ready to buy 2 chickens!
It’s really important to me to have loving chickens who like to be held and don’t mind being picked up. My kids love chasing after and holding chickens.
I'm sorry to be the one to tell you, but this ^ is not really a thing.
A chicken that is chased will run! And the next time they will run sooner and run faster.
If you want your chickens to be tame enough to handle, you can't allow children (or anyone) to chase them.
Instead, you can lure them in with treats. But the amount of petting most chickens will tolerate is limited. And if it's done too tricky multiple times (like they have a bad / uncomfortable / scary experience) they will wisen up and not even come in for treats.
The best kind of pet for little humans is a dog. As I'm sure you must know, dogs can still lose their cool and not be okay with kids if they have been tormented. But that's the most patient creature you will find. A bird is not nearly the same.
Occasionally, a chicken will come along who just happens to like humans. It's a combination of their natural personality and a keeper who lets animals come to them, patiently, and lets them leave the second they show any sign of wanting to go.
If your kids don't have the patience and self-control for that, then even the best chicken in the whole world is going to choose self-preservation and maintaining her dignity over socializing with humans.
I hope this helps you consider what you want out of your chicken journey. Please make sure the minimum number of hens you keep is 3, for important flock dynamics reasons (imagine being stuck with only one person to talk to the rest of your life!). They need friends plural.