Optical motion capture (mocap) requires accurately reconstructing the human body from retroreflective markers, including pose and shape. In a typical mocap setting, marker labeling is an important but tedious and error-prone step. Previous work has shown that marker labeling can be automated by using a structured template defining specific marker placements, but this places additional recording constraints. We propose to relax these constraints and solve for Unstructured Unlabeled Optical (UUO) mocap. Compared to the typical mocap setting that either labels markers or places them w.r.t a structured layout, markers in UUO mocap can be placed anywhere on the body and even on one specific limb (e.g., right leg for biomechanics research), hence it is of more practical significance. It is also more challenging. To solve UUO mocap, we exploit a monocular video captured by a single RGB camera, which does not require camera calibration. On this video, we run an off-the-shelf method to reconstruct and track a human individual, giving strong visual priors of human body pose and shape. With both the video and UUO markers, we propose an optimization pipeline towards marker identification, marker labeling, human pose estimation, and human body reconstruction. Our technical novelties include multiple hypothesis testing to optimize global orientation, and marker localization and marker-part matching to better optimize for body surface. We conduct extensive experiments to quantitatively compare our method against state-of-the-art approaches, including marker-only mocap and video-only human body/shape reconstruction. Experiments demonstrate that our method resoundingly outperforms existing methods on three established benchmark datasets for both full-body and partial-body reconstruction.