Context. The first hydrostatic core (FHSC) phase is a brief stage in the protostellar evolution that is difficult to detect. Its chemical composition determine that of later evolutionary stages. Numerical simulations are the tool of choice to study these objects.Aims. Our goal is to characterize the chemical evolution of gas and dust during the formation of the FHSC. Moreover, we are interested in analyzing, for the first time with 3D magnetohydrodynamic (MHD) simulations, the role of grain growth in its chemistry.Methods. We postprocessed 2 × 105 tracer particles from a RAMSES non-ideal MHD simulation using the codes NAUTILUS and SHARK to follow the chemistry and grain growth throughout the simulation.Results. Gas-phase abundances of most of the C, O, N, and S reservoirs in the hot corino at the end of the simulation match the ice-phase abundances from the prestellar phase. Interstellar complex organic molecules such as methyl formate, acetaldehyde, and formamide are formed during the warm-up process. Grain size in the hot corino (nH > 1011 cm−3) increases forty-fold during the last 30 kyr, with negligible effects on its chemical composition. At moderate densities (1010 < nH < 1011 cm−3) and cool temperatures 15 < T < 50 K, increasing grain sizes delay molecular depletion. At low densities (nH ~ 107 cm−3), grains do not grow significantly. To assess the need to perform chemo-MHD calculations, we compared our results with a two-step model that reproduces well the abundances of C and O reservoirs, but not the N and S reservoirs.Conclusions. The chemical composition of the FHSC is heavily determined by that of the parent prestellar core. Chemo-MHD computations are needed for an accurate prediction of the abundances of the main N and S elemental reservoirs. The impact of grain growth in moderately dense areas delaying depletion permits the use of abundance ratios as grain growth proxies.