A recently proposed conformal field theory of string ghosts with quartic interactions is investigated. On a flat world sheet the theory is closely related to the massless Thirring model, but on a curved world sheet it is different. Similarity with the Thirring model allows us to ``solve'' the theory, first by a functional computation of correlation functions, and then by bosonization. Because of differences from the Thirring model, the conformal anomaly and the ghost number anomaly depend on the coupling q. The former is given by 24πTμ μ=[26-27q/(q+π)]R where R is the world-sheet scalar curvature. This result suggests the possibility of using a modified ghost system to construct stringlike theories in space-time dimensions other than 26.