White-dwarf stars are the end product of stellar evolution for most stars in the Universe(1). Their interiors bear the imprint of fundamental mechanisms that occur during stellar evolution(2,3). Moreover, they are important chronometers for dating galactic stellar populations, and their mergers with other white dwarfs now appear to be responsible for producing the type Ia supernovae that are used as standard cosmological candles(4). However, the internal structure of white-dwarf stars-in particular their oxygen content and the stratification of their cores-is still poorly known, because of remaining uncertainties in the physics involved in stellar modelling codes(5,6). Here we report a measurement of the radial chemical stratification (of oxygen, carbon and helium) in the hydrogendeficient white-dwarf star KIC08626021 (J192904.6+444708), independently of stellar-evolution calculations. We use archival data(7,8) coupled with asteroseismic sounding techniques(9,10) to determine the internal constitution of this star. We find that the oxygen content and extent of its core exceed the predictions of existing models of stellar evolution. The central homogeneous core has a mass of 0.45 solar masses, and is composed of about 86 per cent oxygen by mass. These values are respectively 40 per cent and 15 per cent greater than those expected from typical white-dwarf models. These findings challenge present theories of stellar evolution and their constitutive physics, and open up an avenue for calibrating white-dwarf cosmochronology(11).