The temporal purity of single photons is crucial to the indistinguishability of independent photon sources for the fundamental study of the quantum nature of light and the development of photonic technologies. Currently, the technique for single photons heralded from time-frequency entangled biphotons created in nonlinear crystals does not guarantee the temporal-quantum purity, except using spectral filtering. Nevertheless, an entirely different situation is anticipated for narrow-band biphotons with a coherence time far longer than the time resolution of a single-photon detector. Here we demonstrate temporally pure single photons with a coherence time of 100 ns, directly heralded from the time-frequency entangled biphotons generated by spontaneous four-wave mixing in cold atomic ensembles, without any supplemented filters or cavities. A near-perfect purity and indistinguishability are both verified through Hong-Ou-Mandel quantum interference using single photons from two independent cold atomic ensembles. The time-frequency entanglement provides a route to manipulate the pure temporal state of the single-photon source. DOI: 10.1103/PhysRevLett.117.013602 The purity of the quantum state of a single photon is a prerequisite of its indistinguishability with single photons from other independent sources, and the latter is an essential basis for the realization of a scalable quantum network with distant and independent nodes [1][2][3][4][5]. Furthermore, the temporal purity of a single photon is crucial to the development of photonic technologies for quantum information science [6,7]. The traditional method to produce indistinguishable single photons is heralding time-frequency entangled biphotons generated from spontaneous parametric down-conversion (SPDC) in a nonlinear crystal which is pumped by ultrashort pulses [4,5,8]. In recent decades many new physical systems have been developed [9-13] to obtain pure single photons without time-frequency entanglement built in.In the community of quantum communication, SPDC in Ď Ă°2Ă nonlinear media is still the preferable way to produce entangled biphotons because of its simplicity in the operation and the potential for on-chip integration and scaling up [14][15][16]. However, the intrinsic feasible phase matching condition of SPDC crystal allows an extremely broad range of temporal modes. Therefore, the typical temporal coherence time of the photon source is of femtosecond scale. Compared to the time response of most commercial single-photon detectors, which is about 1 ns, this temporal coherence time is so short that the trigger photon of the heralded single photon is measured with a large time uncertainty. This time uncertainty damages the temporal quantum purity of the single-photon source. To circumvent the time uncertainty problem due to the slowness of the detectors, a common practice is to use external spectral filtering including passive filtering with narrowband filters [4,5,17] and active filtering with an optical cavity [18]. In this case, the temporal state o...