It can be upsetting for an owner if they think their chickens are fighting or are unhappy, however sometimes what looks like nasty behaviour can actually be mother nature's way of keeping the peace.
If you think about what it actually means, "pecking order" is a chickens way of ensuring the communal harmony of your flock, and helps prevent constant fights to be "top dog".
Depending on whether you have just hens, or hens and cocks, there are three distinct pecking orders that may need to be established - one for the hens, one for the roosters, and one for the hens and roosters.
Once the pecking order has been established (and the establishing bit is where you will see chickens picking on other chickens), they should then live together very happily, unless something disrupts the pecking order. Common causes are overcrowding and adding new birds. Always try and make sure your lower ranking birds have somewhere to run and escape to and they should sort themselves out with the minimum of fuss.
You only need to worry if the chicken at the bottom of the pecking order is being seriously deprived of food and water or seriously pecked and wounded. This, however, is rare, and usually settles down within a few weeks, so wait at least fourteen days before taking any action (unless the chicken is being hurt).
If the chicken is having real problems getting to the food or water then try adding more food bowls to the coop (or wherever they spend most their time). Add enough food bowls so there is one food bowl and one water bowl for every two birds, and two bowls (two food bowls and two water containers) if there are three chickens. This way, the runty chicken will be able to run from one food bowl to another without being scolded too much!
If the chicken is being physically hurt then it will need seperating until it is fully healed: divide the coop with mesh so the chickens can see each other but can't physically touch each other. After leaving them like this for one week, try taking away the mesh and seeing what happens. Make sure you are there for when they are re-introduced. If, on their first visit, the chicken attacks the other chicken, pick them both up and hold them so they are facing each other. Seperate them again but, every day, hold them face to face and put them in a strange place (eg. in a room in the house) for perhaps half an hour a day.
However, if one chicken is still behaving aggressively to the other, then it will either have to fend for itself or you will have to release it to another family :-(
When you introduce a new chicken to the flock, especially if it's younger than the others, then it will automatically be placed at the bottom of the pecking order (this happened to Milly). The new chicken will be pecked a few times, but leave the new chicken alone (unless it is injured). The aggressive behaviour may last longer when a new chicken is introduced, but nature usually sorts it out in the end.