Yes, chickens are quite unwelcoming to new birds without a long introductory period and it can result in injuries and worse. You'll want to set up a look but no touch arrangement where they can see your new bird without harming it. You want them totally bored and uninterested in one another; can take several weeks or longer. By the time they all seem non-reactive to each other and they are allowed full contact, make sure there's as much space as possible (to evade bullying attempts), extra feed and water locations (so original birds can't guard all the resources and starve the newcomer), and lots of clutter to use for hiding and escape if things go south.
It is more difficult to introduce just one new bird as they will have no one else to split their negative attentions. I'd expect this to take more than a month, but all bird flocks are unique.
Best of luck!