Sulfoxylic acid (HOSOH), a chemical intermediate roughly midway along the path between highly reduced (H2S) and highly oxidized sulfur (H2SO4), has been detected using Fourier transform microwave spectroscopy and double resonance techniques, guided by new high-level CCSD(T) quantum-chemical calculations of its molecular structure. Rotational spectra of the two most stable isomers of HOSOH, the putative ground state with C2 symmetry and the low-lying C(s) rotamer, have been measured to high precision up to 71 GHz, allowing accurate spectroscopic parameters to be derived for both isomers. HOSOH may play a role in atmospheric and interstellar chemistry, and the present work provides the essential data to enable remote sensing and/or radioastronomical searches for these species. Spectroscopic characterization of HOSOH suggests that other transient intermediates in the oxidation of SO2 to H2SO4 may be amenable to laboratory detection as well.