Simulations of the thermal and dynamical evolution of primordial gas typically focus on the role played by H2 cooling. H2 is the dominant coolant in low-density primordial gas and it is usually assumed that it remains dominant at high densities. However, H2 is not an effective coolant at high densities, owing to the low critical density at which it reaches local thermodynamic equilibrium and to the large opacities that develop in its emission lines. It is therefore important to quantify the contribution made to the cooling rate by emission from the other molecules and ions present in the gas. A particularly interesting candidate is the H3+ ion, which is known to be an effective coolant at high densities in planetary atmospheres. In this paper, we present results from simulations of the thermal and chemical evolution of gravitationally collapsing primordial gas, which include a detailed treatment of H3+ chemistry and an approximate treatment of H3+ cooling. We show that in most cases, the contribution from H3+ is too small to be important, but if a sufficiently strong ionizing background is present, then H3+ cooling may become significant.