NEATH (Non-Equilibrium Abundances Treated Holistically) is a framework for post-processing hydrodynamical simulations with a time-dependent chemical network. It has been calibrated to return abundances consistent with the underlying hydro simulations for species which are imporant for the thermal evolution of the gas. The abundances of hundreds of additional species, many of which are important observational tracers of star-forming regions, are also calculated at a low computational cost. Details of the NEATH framework are described in this paper. Source code and example data are available here.