A noteworthy feature of the high-temperature superconductors is the unconventional symmetry of the superconducting order parameter. Several experiments(1-3) have established that the order parameter has a four-fold d(x2-y2) symmetry under rotation of the lattice (the order parameter of conventional superconductors is, in contrast, isotropic). An intriguing and much debated possibility is that, in certain cases, an additional imaginary component might be present, having an isotropic s-wave(4-6) or d(xy) symmetry(7-1)0. A consequence of a complex order parameter of the form d(x2-y2) + id(xy) is that it would break both reflection (parity, P) symmetry and time-reversal (T) symmetry, a clear signature of which would be the spontaneous appearance of a macroscopic magnetization at the superconducting transition temperature. Broken T symmetry has been reported(5,11), but searches for the effects of combined P and T symmetry breaking have so far yielded null results(12-15). Here we report the observation of a weak (similar to 10(-5) gauss) magnetic field that appears spontaneously at the superconducting transition temperature of epitaxial thin films of YBa2Cu3O7-delta. The magnetic signal originates near the edges of the samples. One interpretation for this observation is that the order parameter carries an intrinsic angular momentum, related to the breaking of P and T symmetries, but other possibilities cannot yet be excluded.