Mystery "organ" on the underside of chicken thighs?
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.