Abstract We report the discovery of PSR J1757−1854, a 21.5-ms pulsar in a highly-eccentric, 4.4-h orbit with a neutron star (NS) companion. PSR J1757−1854 exhibits some of the most extreme relativistic parameters of any known pulsar, including the strongest relativistic effects due to gravitational-wave damping, with a merger time of 76 Myr. Following a 1.6-yr timing campaign, we have measured five post-Keplerian parameters, yielding the two component masses (mp = 1.3384(9) M⊙ and mc = 1.3946(9) M⊙) plus three tests of general relativity, which the theory passes. The larger mass of the NS companion provides important clues regarding the binary formation of PSR J1757−1854. With simulations suggesting 3-σ measurements of both the contribution of Lense–Thirring precession to the rate of change of the semimajor axis and the relativistic deformation of the orbit within ∼7–9 yr, PSR J1757−1854 stands out as a unique laboratory for new tests of gravitational theories.