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Asteroseismic ‘sounding’ reveals the internal chemical stratification of the white dwarf KIC08626021, which has a central homogeneous core—composed of 86 per cent oxygen—that has a mass of 0.45 solar masses. White-dwarf stars are the end point of stellar evolution for most stars, and the merger of two of these bodies seems to be responsible for the type Ia supernovae used in cosmology. The interior structure of white-dwarf stars, however, is not well known. Noemi Giammichele and collaborators have used archival data and asteroseismic sounding methods to determine that the hydrogen-deficient white dwarf KIC08626021 contains a central homogeneous core that has a mass of 0.45 solar masses and is 86% oxygen. The core is larger, and the oxygen fraction higher, than predicted by standard models. White-dwarf stars are the end product of stellar evolution for most stars in the Universe1. Their interiors bear the imprint of fundamental mechanisms that occur during stellar evolution2,3. 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 candles4. 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 codes5,6. Here we report a measurement of the radial chemical stratification (of oxygen, carbon and helium) in the hydrogen-deficient white-dwarf star KIC08626021 (J192904.6+444708), independently of stellar-evolution calculations. We use archival data7,8 coupled with asteroseismic sounding techniques9,10 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 cosmochronology11.