We present results obtained with a three-dimensional, Lyα radiative transfer code applied to a fully cosmological galaxy formation simulation. The developed Monte Carlo code is capable of treating an arbitrary distribution of source Lyα emission, neutral hydrogen density, temperature, and peculiar velocity of the interstellar medium. We investigate the influence of resonant scattering on the appearance and properties of young galaxies by applying the code to a simulated "Lyman break galaxy" at redshift z = 3.6, star formation rate 22 M yr^-1, and total Lyα luminosity 2.0 × 10⁴³ ergs s^-1. It is found that resonant scattering of Lyα radiation can explain that young galaxies are frequently observed to be more extended on the sky in Lyα than in the optical. Moreover, it is shown that, for the system investigated, due to the anisotropic escape of the photons, the observed maximum surface brightness can differ by more than an order of magnitude, and the total derived luminosity by a factor of ~4, depending on the orientation of the system relative to the observer.