We report evidence for superconductivity in undoped La2CuO4 obtained from resistivity, thermoelectric power, and susceptibility measurements. The onset temperature is near 40 K and we have determined its pressure and field dependence in resistivity. The superconducting behavior is of a trace and filamentary nature and is quite sensitive to stoichiometry. Its occurrence is extremely process dependent and an be controlled by oxygen pressure. We discuss several likely sources for the superconducting activity. © 1987 The American Physical Society.