Electrochemical CO reduction can potentially serve as an intermediate step for the efficient conversion of CO2 to chemical fuels using renewable electricity. While membrane electrode assembly (MEA) CO electrolyzers are industrially relevant, they currently suffer from a low energy efficiency due to a high cell voltage (typically > 3 V at 1,000 mA cm-2). In this work, we reveal that water and hydroxide transport at the quasi two-phase interface of the cathode limits the performance of MEA electrolyzers at high current densities. By developing a system that allows for sufficiently rapid interfacial mass transport, we obtain an electrolyzer that has a cell voltage of only 2.4 V at 1,000 mA cm-2. The electrolyzer has a Faradaic yield of more than 90% for C2+ products, and demonstrates a stability of more than 100 h.