My little son just asked me this question. His mother used to complain about the excruciating pain she suffered when she gave birth to him. He is a compassionate kid and wonders whether the hen goes through this pain everyday. Not being a hen, I am not sure if chickens experience pain that is close to the pain associated with giving birth.
We really don't know - we can't really ask the chicken. At least, it's unlikely it's as painful as it can be with humans.
The reason human birth is (or can be) very painful is that the human baby's head has to fit through the woman's pelvis. Since splitting from chimpanzees, human heads have gotten bigger, while the pelvis has gotten more narrow due to adapting to walking on two legs. While chimpanzees give birth in an average of around 2 hours, humans can take over a day to do so, and the baby being too big can lead to maternal and natal death.
Back to chickens, while there are different sizes of eggs, the larger eggs come from larger chicken breeds. If it does hurt them, at least it takes a lot less time - only a few minutes. From personal experience, the hens do not appear traumatized even seconds afterwards and just go about their day as soon as the egg is out.