"Kosher" is the process, not the bird. There are animals that are not kosher--i.e. pigs, camels, birds of prey, shellfish--but chickens are a clean animal while they are alive, and if they are processed correctly.
Kosher processing involves first of all, that the animal was not 'torn in the field'--it does not have any injury or disease at the time of processing. Then it must be killed in a way that it is bled out as completely as possible, generally by severing the arteries in the neck. The blood must be buried in the dirt; it cannot be collected and used for anything. (regular slaughter plants often collect their animal blood for use in various products like pet food) After it is gutted and plucked, the animal is soaked in salt water and rinsed thoroughly to remove any blood still left. It is scripturally forbidden in the Torah to consume animals with the blood in them. On mammals, the sciatic nerve in the hindquarters must be removed, as well as certain fats around the internal organs which are not allowed to be consumed. Also, all utensils and surfaces used must be ceremonially clean--they cannot process a kosher animal on the same equipment used for an unkosher slaughter/butchering, because it would be rendered unclean by doing so, and if clean food touches unclean things, it becomes unclean. And if it is done commercially, a rabbi must oversee the slaughterhouse to be sure it is done correctly, and then the rabbi will put his stamp of approval (called a hechshur) on the product. For any commercially packaged food to be kosher, it must have rabbinical supervision and carry one of these marks. Kosher foods thus have a much higher standard of cleanliness and purity than the USDA's standards, in most cases. (The USDA actually has a standard for how much rodent or insect can be contained in something like peanut butter before it is unsafe, it is actually acceptable if a rat accidentally falls into the food and gets mashed in sometimes; whereas the Orthodox Union will not allow a kosher label to be placed on a food product if the factory has a known infestation with pests.)
I have heard there is a chicken being referred to as a "Kosher King" but I am unaware of what breed/hybrid this really is.
