The atomic structure of the Ni(110)4 x 1-S reconstruction has been determined on the basis of surface X-ray diffraction measurements. An analysis of the in-plane diffraction data shows that the model consists of Ni rows along the  direction, two for every 4 x 1 unit cell, corresponding to 0.5 ML Ni coverage. The S is chemisorbed in pseudo two-fold hollow sites both on the Ni rows and in the troughs between the rows with a S coverage of 0.75 ML. Furthermore, rod-scans along fractional-order reflections reveal sub-surface relaxations. The results are in good agreement with recent STM and previous AES and radioactive tracer studies.