Open Radio Access Network (O-RAN) offers a new paradigm for the design and deployment of future RANs. The unique architecture of O-RAN presents two main challenges when designing a scheduler. First, it is impractical to obtain accurate and full Channel State Information (CSI) due to estimation errors and limited bandwidth of the fronthaul link between Open Radio Unit (O-RU) and Open Distributed Unit (O-DU). Second, the large-scale processing at an O-DU introduces difficulties in meeting the stringent time requirement in O-RAN, especially in the real-time (RT) control loop. To address these challenges, we propose R-3-a real-time robust Multi-user, Multiple Input, Multiple Output (MU-MIMO) scheduler for O-RAN. R3 serves as a comprehensive scheduling solution encompassing RB allocation, MCS selection, and beamforming calculation. Most notably, R(3)utilizes a limited number of CSI samples to offer probabilistic QoS guarantees. To meet the timing requirements of O-RAN, R-3 decomposes the scheduling problem into two distinct sub-problems and integrates them into separate control loops. Moreover, each sub-problem is designed with a parallel structure, utilizing a reduced search space, and implemented on a GPU platform to accelerate the computation time. Experimental results demonstrate that R(3)offers competitive throughput performance as the state-of-the-art while simultaneously fulfilling the QoS guarantees. Further, R(3)meets the timing requirements of various control loops in O-RAN over a wide range of operating conditions.