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Single atoms or atom-like emitters are the purest source of single photons, they are intrinsically incapable of multi-photon emission. To demonstrate this degree of photon number-state purity we have realized a single-photon source using a single ion trapped at the common focus of high numerical aperture lenses. Our trapped-ion source produces single-photon pulses with without any background subtraction. After subtracting detector dark counts the residual is less than 3 × 10−4 (95% confidence interval). The multi-photon component of the source light field is low enough that we measure violation of a quantum non-Gaussian state witness, by this characterization the source output is indistinguishable from ideal attenuated single photons. In combination with efforts to enhance collection efficiency from single emitters, our results suggest that single trapped ions are not only ideal stationary qubits for quantum information processing, but promising sources of light for scalable optical quantum networks. [ABSTRACT FROM AUTHOR]