We investigate the impact of realistic three-dimensional (3D) hydrodynamical model stellar atmospheres on the determination of elemental abundances in the carbon-rich, hyper-iron-poor stars HE 0107-5240 and HE 1327-2326. We derive the chemical compositions of the two stars by means of a detailed 3D analysis of spectral lines under the assumption of local thermodynamic equilibrium (LTE). The lower temperatures of the line-forming regions of the hydrodynamical models cause changes in the predicted spectral line strengths. In particular, we find the 3D abundances of C, N, and O to be lower by about -0.8 dex (or more) than estimated from a 1D analysis. The 3D abundances of iron peak elements are also decreased but by smaller factors (about -0.2 dex). We caution, however, that the neglected non-LTE effects might actually be substantial for these metals. We finally discuss possible implications for studies of early Galactic chemical evolution.