Global acquisition of atmospheric wind profiles using a spaceborne direct-detection Doppler wind lidar is being accomplished following the launch of European Space Agency's Aeolus mission. One key part of the instrument is a single-frequency, ultraviolet laser that emits nanosecond pulses into the atmosphere. High output energy and frequency stability ensure a sufficient signal-to-noise ratio of the backscatter return and an accurate determination of the Doppler frequency shift induced by the wind. This Letter discusses the design of the laser transmitter for the first Doppler wind lidar in space and its performance during the first year of the Aeolus mission, providing valuable insights for upcoming space lidar missions.