We present the first implementation of a Multi-User Multiple-Input Multiple-Output (MU-MIMO) transmission scheme on the Physical Downlink Shared Channel (PDSCH) for 5G Open Radio Access Network (O-RAN) based on OpenAirInterface (OAI). Our implementation features a fully functional O-RAN-compliant 5G New Radio (5G NR) system, including a 5G Core Network (5G CN), a refined 5G RAN, which is split into a Centre Unit (CU) and an Distributed Unit (DU), and 5G NR User Equipment (UEs). This implementation demonstrates MU-MIMO performance in the downlink while showcasing the disaggregation capabilities of O-RAN. Specifically, the Base Station (i.e. gNB) in our setup is capable of serving two UEs simultaneously over the same downlink Resource Block (RBs). User scheduling is performed based on the Precoding Matrix Indicators (PMIs) reported by the UEs according to the NR Channel State Information (CSI) reporting procedure. The system throughput performance is evaluated using $\textit{iperf}$. The obtained results via simulation and testbed experiments demonstrate that the MU-MIMO scheme achieves significant downlink throughput gains, particularly in the high Signal-to-Noise-Ratio (SNR) regime, while keeping the Block Error Rate (BLER) below the required threshold of $10^{-1}$ for both UEs.