Silkie chickens are a highly-prized breed of chicken that has beautiful silky white plumage, and startlingly black skin. They are frequently found in China, India, and Southeast Asia. They have a mild-mannered nature and make excellent pets, and you'll often see them at poultry shows.
The chicken flesh itself is a dark bluish-grey or even black, and the bones are black as well. But the meat really doesn't taste different by nature; it's just chicken. The one difference, however, comes from the way the birds are raised. These obviously aren't factory-farmed birds, raised on the enormous scale of US poultry farms, so they're almost invariably free-range and slightly gamier in flavor. In fact, if you're looking for free-range and well-raised birds, choosing a black chicken is a good way to go.
Do you ever eat black chicken? How do you cook it? It seems that a roasted black bird would be slightly startling to guests; perhaps you're better off with soup? Here's a recent article from the New York Times on black chicken and soup: