In primordial gas, molecular hydrogen forms primarily through associative detachment of H À and H, thereby destroying the H À . The H À anion can also be destroyed by a number of other reactions, most notably by mutual neutralization with protons. However, neither the associative detachment nor the mutual neutralization rate coefficients are well determined: both may be uncertain by as much as an order of magnitude. This introduces a corresponding uncertainty into the H 2 formation rate, which may have cosmological implications. Here we examine the effect that these uncertainties have on the formation of H 2 and the cooling of protogalactic gas in a variety of situations. We show that the effect is particularly large for protogalaxies forming in previously ionized regions, affecting our predictions of whether or not a given protogalaxy can cool and condense within a Hubble time, and altering the strength of the ultraviolet background that is required to prevent collapse.