The discovery of high-temperature superconductivity in doped copper oxides, which in their insulating forms are nearly ideal two-dimensional spin-1/2 Heisenberg antiferromagnets, has stimulated great interest in finding additional examples of such magnetic systems. We find that Sr[sub 2]IrO[sub 4], which has the K[sub 2]NiF[sub 4] structure and should have a 5[ital d][sup 5] low-spin ([ital S]=1/2) electronic configuration, develops a ferromagnetic moment near 250 K. The small size of the remanent moment (10[sup [minus]2][mu][sub [ital B]]), and our structural studies, however, imply that this is weak ferromagnetism which appears at the Neel temperature due to a Dzyaloshinsky-Moriya interaction, in a manner analogous to that seen in La[sub 2]CuO[sub 4].