We investigate molecular evolution from a molecular cloud core to a first hydrostatic core in three spatial dimensions. We perform a radiation hydrodynamic simulation in order to trace fluid parcels, in which molecular evolution is investigated, using a gas-phase and grain-surface chemical reaction network. We derive spatial distributions of molecular abundances and column densities in the core harboring the first core. We find that the total of gas and ice abundances of many species in a cold era (10 K) remain unaltered until the temperature reaches ~500 K. The gas abundances in the warm envelope and the outer layer of the first core (T < 500 K) are mainly determined via the sublimation of ice-mantle species. Above 500 K, the abundant molecules, such as H2CO, start to be destroyed, and simple molecules, such as CO, H2O and N2 are reformed. On the other hand, some molecules are effectively formed at high temperature; carbon-chains, such as C2H2 and cyanopolyynes, are formed at the temperature of >700 K. We also find that large organic molecules, such as CH3OH and HCOOCH3, are associated with the first core (r < 10 AU). Although the abundances of these molecules in the first core stage are comparable or less than in the protostellar stage (hot corino), reflecting the lower luminosity of the central object, their column densities in our model are comparable to the observed values toward the prototypical hot corino, IRAS 16293-2422. We propose that these large organic molecules can be good tracers of the first cores.