Hi, welcome to BYC!That is normal behaviour! She just wants to make sure the friend knows she is the top chick! It will settle. Though bantam size chickens are usually a little more persistent to go on in this type of behaviour a bit longer than standard size chickens. So just be prepared for that. Bantams are strong and high spirited. They will very often even challenge my full size chickens.
Also did you get her some dirt or much better than dirt is a low Rubbermaid container of sand! She need help digesting her food so she does not have those low days or droopy days. If she works to hard digesting her food she won't be putting as much into her eggs.
She will eat the sand plus sand bath in it! She will love love love it. You will make her one very very happy chicken! Happiness equals better eggs and better digestion!

My chickens do eat the sand but they will not bath in it at all.
Yes, things actually usually get the worst right at roost time. They fight for the safest place to sleep, even in nature. So, many people put the new chicken on roost after dark after they've seen each other through a fence for weeks. Not eating at the same time is normal. So it will be important to make sure whoever is eating last is still getting their share of the combined nutrients. It is normal for the top chicken to run others off the food. The lowers will run around and eat anyways. The pecking is normal. It should calm down within a few days. As long as there is no blood shed, they are good. If you do separate them make sure they can see each other, otherwise the whole process starts over again. It is important that you be persistent and let this play out. Chicky will be happier forever with a friend. Chickens are flock animals and need friends. Tight quarters will make this possibly more difficult.... but you are working with what you have right now!
Hang in there. If you provide extra treats, not too many but make them high protein.
Do you know the age, gender, and breed of your new chicken? I thought Chicky is a Golden Campine. Is she bantam and I never noticed? Or your new chicken?
Keep that chicken!
