It has been shown that rotational lines observed in the Horsehead nebula photodissociation region (PDR) are probably not caused by l-C3H+, as was originally suggested. In the search for viable alternative candidate carriers, quartic force fields are employed here to provide highly accurate rotational constants, as well as fundamental vibrational frequencies, for another candidate carrier: 1(1)A'C3H-. The ab initio computed spectroscopic constants provided in this work are, compared to those necessary to define the observed lines, as accurate as the computed spectroscopic constants for many of the known interstellar anions. Additionally, the computed D-eff for C3H is three times closer to the D deduced from the observed Horsehead nebula lines relative to l-C3H+. As a result, 1(1)A'C3H- is a more viable candidate for these observed rotational transitions. It has been previously proposed that at least C6H- may be present in the Horsehead nebular PDR formed by way of radiative attachment through its dipole-bound excited state. C3H- could form in a similar way through its dipole-bound state, but its valence excited state increases the number of relaxation pathways possible to reach the ground electronic state. In turn, the rate of formation for C3H- could be greater than the rate of its destruction. C3H- would be the seventh confirmed interstellar anion detected within the past decade and the first CnH- molecular anion with an odd n.