There is a small, round, black "organ" under chicken thighs, and some people like to eat it. Identifying this seems to be quite the lingering Internet mystery.
They are there on prepared fried chicken–specifically Popeye's, but I'm sure it's there on any prepared bone-in chicken thigh. I've read various claims that it's the "oyster", liver, kidney, or a blood vessel. By "under" the thigh, I mean that it's found on the bony side opposite the meat.
See these pages: 1, 2, 3. There are tons more if you search.
Photos follow: Chicken thigh with gizzard thing exposed, then removed, then cross section.
Best Answer
As discussed in the comments under the question, I believe the organ in question is a kidney, from the pocket in the pelvis of a thigh butchered in a fairly unusual manner, with that part of the pelvis still attached.
See page 3.21 in the University of Kentucky's PDF of Chapter 3 of Chicken Anatomy and Physiology. It shows where the kidney's are in the chicken (moderately graphic), and the shape looks quite similar to the mystery item in the original question's photographs, allowing for shrinkage from cooking.