We present chemical abundance measurements of three stars in the ultrafaint dwarf galaxy Horologium I, a Milky Way satellite discovered by the Dark Energy Survey. Using high-resolution spectroscopic observations, we measure the metallicity of the three stars, as well as abundance ratios of several {alpha}-elements, iron-peak elements, and neutron-capture elements. The abundance pattern is relatively consistent among all three stars, which have a low average metallicity of [Fe/H]~-2.6 and are not {alpha}-enhanced ([{alpha}/Fe]~0.0). This result is unexpected when compared to other low-metallicity stars in the Galactic halo and other ultrafaint dwarfs and suggests the possibility of a different mechanism for the enrichment of Hor I compared to other satellites. We discuss possible scenarios that could lead to this observed nucleosynthetic signature, including extended star formation, enrichment by a Population III supernova, and or an association with the Large Magellanic Cloud.