White dwarfs are the burnt out cores of Sun-like stars and are the final fate of 97% of all stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements, apart from the lightest ones, to settle out of their atmospheres. The most direct method to probe the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present the first known pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the light curve, independent of the pulsations. This 0.325M$_⊙$ white dwarf --- one member of SDSS J115219.99+024814.4 --- will serve as a powerful benchmark to constrain empirically the core composition of low-mass stellar remnants and investigate the effects of close binary evolution on the internal structure of white dwarfs.