A major research area in Computer Assisted Intervention (CAI) is to aid laparoscopic surgery teams with Augmented Reality (AR) guidance. This involves registering data from other modalities such as MR and fusing it with the laparoscopic video in real-time, to reveal the location of hidden critical structures. We present the first system for AR guided laparoscopic surgery of the uterus. This works with pre-operative MR or CT data and monocular laparoscopes, without requiring any additional interventional hardware such as optical trackers. We present novel and robust solutions to two main sub-problems: the initial registration, which is solved using a short exploratory video, and update registration, which is solved with real-time tracking-by-detection. These problems are challenging for the uterus because it is a weakly-textured, highly mobile organ that moves independently of surrounding structures. In the broader context, our system is the first that has successfully performed markerless real-time registration and AR of a mobile human organ with monocular laparoscopes in the OR.