The absorption spectrum of the propargyl radical in the region from 180 to 400 nm is investigated in detail by means of theory. Vertical excitation energies and potential energy surfaces are determined by highly accurate multireference configuration interaction (MRCI) calculations. The vibrational dynamics of several electronic states is studied, and line intensities and positions are calculated with respect to the electronic and vibrational ground state. Four electronic states absorb in the region of interest: 1 2B2, 2 2B1, 2 2B2, and 3 2B1. However, electronic excitations into the 2B2 states are dipole-forbidden from the X 2B1 ground state and corresponding vibronically allowed transitions are shown to be weak. The spectrum is dominated by the strong 2 2B1 <-- 1 2B1 band which is computed in overall good agreement with available experiments. A strong absorption at 242 nm, which has been assigned to propargyl, is not confirmed by the calculations, and only very weak absorptions are found at wavelengths shorter than 280 nm. The present results strongly suggest that the 242 nm feature must be due to a different species.