Molecular calculations without assuming the Born-Oppenheimer (BO) approximation present a level of complexity which is much higher than in calculations where the BO approximation is assumed and the nuclei are stationary. In this report we discuss how non-BO calculations can be carried out for a system with three nuclei and three electrons, i.e. H3. In particular, the problem of basis set selection that is critical to achieving high accuracy in such calculations is discussed. As an illustration a smallscale non-BO calculations of H3 are presented and discussed.