Symbiotic star surveys have traditionally relied almost exclusively on low resolution optical spectroscopy. However, we can obtain a more reliable estimate of their total Galactic population by using all available signatures of the symbiotic phenomenon. Here we report the discovery of a hard X-ray source, 4PBC J0642.9+5528, in the Swift hard X-ray all-sky survey, and identify it with a poorly studied red giant, SU Lyn, using pointed Swift observations and ground-based optical spectroscopy. The X-ray spectrum, the optical to UV spectrum, and the rapid UV variability of SU Lyn are all consistent with our interpretation that it is a symbiotic star containing an accreting white dwarf. The symbiotic nature of SU Lyn went unnoticed until now, because it does not exhibit emission lines strong enough to be obvious in low resolution spectra. We argue that symbiotic stars without shell-burning have weak emission lines, and that the current lists of symbiotic stars are biased in favor of shell-burning systems. We conclude that the true population of symbiotic stars has been underestimated, potentially by a large factor.