Before the first stars formed, helium was the first neutral atom by combining with free electrons, due to its higher ionization potential; this formation was quickly followed by the formation of helium hydride. As helium hydride’s formation and ensuing destruction creates a path for atomic hydrogen to form molecular hydrogen, its abundance contributes to gravitational collapse and star formation, and the emission line indicating its presence in interstellar space was only recently detected, it is of interest to astrophysicists studying the early universe. Because radiative association is the dominant formation reaction for helium hydride at all redshifts, and many early universe chemistry models rely on accurate results for calculations of destruction rates, this project explicitly calculated the rovibrationally distinguished partial cross sections and rate coefficients of helium hydride formation via radiative association, and modeled the abundance of helium hydride in the early universe using recently published and calculated rate coefficients for all relevant formation and destruction reactions. The newly calculated rate coefficients show good agreement with several previous calculations performed using the total cross section and disagree with other recently published results that included arbitrary scale factors to attempt to match observed data. The newly calculated rates predict increased abundance of helium hydride in the early universe, particularly at redshifts below z=200; together with newly reported rates for other reactions, we expect that the abundance of helium hydride is at least two orders of magnitude larger than previous predictions for redshifts below z=20.