We report the discovery of a new class of hydrogen-deficient stars: white dwarfs with an atmosphere primarily composed of carbon, with little or no trace of hydrogen or helium. Our analysis shows that the atmospheric parameters found for these stars do not fit satisfactorily in any of the currently known theories of post-asymptotic giant branch (AGB) evolution, although these objects might be the cooler counter-part of the unique and extensively studied PG 1159 star H1504+65. These stars, together with H1504+65, might thus form a new evolutionary post-AGB sequence.