Observations of nearby galaxies have firmly established, over a broad range of galactic environments and metallicities, that star formation occurs exclusively in the molecular phase of the interstellar medium (ISM). Theoretical models show that this association results from the correlation between chemical phase, shielding, and temperature. Interstellar gas converts from atomic to molecular only in regions that are well shielded from interstellar ultraviolet (UV) photons, and since UV photons are also the dominant source of interstellar heating, only in these shielded regions does the gas become cold enough to be subject to Jeans instability. However, while the equilibrium temperature and chemical state of interstellar gas are well-correlated, the time scale required to reach chemical equilibrium is much longer than that required to reach thermal equilibrium, and both timescales are metallicity-dependent. Here I show that the difference in time scales implies that, at metallicities below a few percent of the Solar value, well-shielded gas will reach low temperatures and proceed to star formation before the bulk of it is able to convert from atomic to molecular. As a result, at extremely low metallicities, star formation will occur in a cold atomic phase of the ISM rather than a molecular phase. I calculate the observable consequences of this result for star formation in low metallicity galaxies, and I discuss how some current numerical models for H2-regulated star-formation may need to be modified.