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We report the discovery of PSR J1757$-$1854, a 21.5-ms pulsar in ahighly-eccentric, 4.4-h orbit around a neutron star (NS) companion. PSRJ1757$-$1854 exhibits some of the most extreme relativistic parameters of anyknown pulsar, including the strongest relativistic effects due togravitational-wave (GW) damping, with a merger time of 76 Myr. Following a1.6-yr timing campaign, we have measured five post-Keplerian (PK) parameters,yielding the two component masses ($m_\text{p}=1.3384(9)\,\text{M}_\odot$ and$m_\text{c}=1.3946(9)\,\text{M}_\odot$) plus three tests of general relativity(GR), which the theory passes. The larger mass of the NS companion providesimportant clues regarding the binary formation of PSR J1757$-$1854. Withsimulations suggesting 3-$\sigma$ measurements of both the contribution ofLense-Thirring precession to the rate of change of the semi-major axis and therelativistic deformation of the orbit within $\sim7-9$ years, PSR J1757$-$1854stands out as a unique laboratory for new tests of gravitational theories.

The High Time Resolution Universe Pulsar Survey - XIII. PSR J1757-1854, the most accelerated binary pulsar