The high-resolution photoelectron spectrum of ArO(-) was obtained using slow electron velocity-map imaging (SEVI). The SEVI spectrum reveals well-resolved vibrational transitions between multiple electronic states of ArO(-) and ArO, both of which are open-shell species. These transitions occur within the broad envelope of previous lower resolution photoelectron spectra. Detailed assignments are made by comparison with theoretical simulations based on high level ab initio calculations and an atoms-in-molecule model that accounts for spin-orbit coupling in the anion and neutral. The adiabatic electron affinity of ArO is found to be 12481 +/- 2 cm(-1). Several ArO(-) and ArO vibrational frequencies and excited-state term energies are accurately determined from the analysis of the experimental spectra and are found to be in excellent agreement with the calculated values.