Atomic clocks, which lock the frequency of an oscillator to the extremely stable quantized energy levels of atoms, are essential for navigation applications such as deep space exploration1 and global navigation satellite systems2, and are useful tools with which to address questions in fundamental physics3-6. Such satellite systems use precise measurement of signal propagation times determined by atomic clocks, together with propagation speed, to calculate position. Although space atomic clocks with low instability are an enabling technology for global navigation, they have not yet been applied to deep space navigation and have seen only limited application to space-based fundamental physics, owing to performance constraints imposed by the rigours of space operation7. Methods of electromagnetically trapping and cooling ions have revolutionized atomic clock performance8-13. Terrestrial trapped-ion clocks operating in the optical domain have achieved orders-of-magnitude improvements in performance over their predecessors and have become a key component in national metrology laboratory research programmes13, but transporting this new technology into space has remained challenging. Here we show the results from a trapped-ion atomic clock operating in space. On the ground, NASA's Deep Space Atomic Clock demonstrated a short-term fractional frequency stability of 1.5 × 10-13/τ1/2 (where τ is the averaging time)14. Launched in 2019, the clock has operated for more than 12 months in space and demonstrated there a long-term stability of 3 × 10-15 at 23 days (no drift removal), and an estimated drift of 3.0(0.7) × 10-16 per day. Each of these exceeds current space clock performance by up to an order of magnitude15-17. The Deep Space Atomic Clock is particularly amenable to the space environment because of its low sensitivity to variations in radiation, temperature and magnetic fields. This level of space clock performance will enable one-way navigation in which signal delay times are measured in situ, making near-real-time navigation of deep space probes possible18.