Chicken with black feather, black meat and black beak is real. There is a breed called Ayam Cemani in Indonesia which is completely black in color. Similar breed is available in India too in the name of Kadaknath. In southern part of India, it's called as Karinkozhi.
However, the eggs of these breeds are not black in color. They are cream+light pink in color. If you have seen black eggs along with the black chicken rooster or hens, then it's fake. Most probably, those eggs are from Emu.
Here is a detailed article: http://thefakebuster.com/199/black-chicken-egg-meat-feather-beak-skin
UPDATE: Plastic eggs, fake eggs and synthetic eggs from China are hoax. You can read more about fake eggs here: http://thefakebuster.com/226/fake-eggs-plastic-eggs-synthetic-eggs-china-real-fake/