An ideal emitter of entangled photon pairs combines the perfect symmetry of an atom with the convenient electrical trigger of light sources based on semiconductor quantum dots. Our source consists of strain-free GaAs dots self-assembled on a triangular symmetric (111)A surface. The emitted photons reveal a fidelity to the Bell state as high as 86(+/- 2)% without postselection. We show a violation of Bell's inequality by more than five times the standard deviation, a prerequisite to test a quantum cryptography channel for eavesdropping. Due to the strict nonlocal nature the source can be used for real quantum processing without any postprocessing. The remaining decoherence channel of the photon source is ascribed to random charge and nuclear spin fluctuations in and near the dot.