Low-mass white dwarfs ( LMWDs ) are believed to be exclusive products of binary evolution , as the Universe is not old enough to produce them from single stars . Because of the strong tidal forces operating during the binary interaction phase , the remnant systems observed today are expected to have negligible eccentricities . Here , we report on the first unambiguous identification of a LMWD in an eccentric ( e = 0.13 ) orbit around the millisecond pulsar PSR J2234+0511 , which directly contradicts this picture . We use our spectra and radio-timing solution ( derived elsewhere ) to infer the WD temperature ( T _ { eff } = 8600 \pm 190 K ) , and peculiar systemic velocity relative to the local standard of rest ( \simeq 31 km s ^ { -1 } ) . We also place model-independent constraints on the WD radius ( R _ { WD } = 0.024 ^ { +0.004 } _ { -0.002 } R _ { \odot } ) and surface gravity ( \log g = 7.11 ^ { +0.08 } _ { -0.16 } dex ) . The WD and kinematic properties are consistent with the expectations for low-mass X-ray binary evolution and disfavour a dynamic three-body formation channel . In the case of the high eccentricity being the result of a spontaneous phase transition , we infer a mass of \sim 1.60 M _ { \odot } for the pulsar progenitor , which is too low for the quark-nova mechanism proposed by Jiang et al . ( 2015 ) , and too high for the scenario of Freire & Tauris ( 2014 ) , in which a WD collapses into a neutron star via a rotationally-delayed accretion-induced collapse . We find that eccentricity pumping via interaction with a circumbinary disk is consistent with our inferred parameters . Finally , we report tentative evidence for pulsations which , if confirmed , would transform the star into an unprecedented laboratory for WD physics .