We have studied photoluminescence (PL) observed from single isoelectronic traps formed by nitrogen pairs in nitrogen δ-doped GaAs layers grown on GaAs(1 1 1)A substrates. The PL was composed of a single peak with a narrow linewidth of ∼80 μeV. Polarized PL measurements confirmed that the emission from single isoelectronic traps in nitrogen δ-doped GaAs(1 1 1) is unpolarized irrespective of nitrogen pair arrangements. These results can be explained by in-plane isotropy of the samples, which is consistent with the symmetrical property of GaAs(1 1 1), and demonstrate that utilizing (1 1 1) substrate is an effective means for obtaining unpolarized single photons, which are desirable for the application to quantum cryptography.