We report the discovery of 0.59 s X–ray pulsations from the low–mass X–ray binary , 5.57 hr dipping and eclipsing ADC source 2A 1822–371 . Pulse arrival time analysis indicates a circular orbit with e < 0.03 ( 95 % confidence ) and an asin i for the neutron star of 1.006 ( 5 ) lightseconds , implying a mass function of ( 2.03 \pm 0.03 ) \times 10 ^ { -2 } M _ { \odot } . The barycentric pulse period was 0.59325 ( 2 ) s in 1996.270 and 0.59308615 ( 5 ) s in 1998.205 , indicating an average spin up with \dot { P } / P = ( -1.52 \pm 0.02 ) \times 10 ^ { -4 } { yr } ^ { -1 } . For a magnetic field strength of \sim 1–5 \times 10 ^ { 12 } G as derived from the X–ray spectrum the implied intrinsic X–ray luminosity is \sim 2–4 \times 10 ^ { 37 } { erg s ^ { -1 } } . The pulse amplitude is low , but increases steeply as a function of energy from a sinusoidal amplitude of 0.25 % in 2–5.4 keV to \sim 3 % above 20 keV . We discuss the constraints on the masses of the companion star and the fact that several aspects of the energy spectrum are in qualitative accordance with that of a strongly magnetised neutron star .