Halide perovskites show great potential for a variety of optoelectronic applications. The presence of robust exciton resonance in these materials makes them promising for use in information photonics. In this paper, we demonstrate the possibility of writing and delayed reading of the optical coherence in halide perovskite by the spontaneous (two-pulse) photon echo in MAPbI3 (MA+ = CH3NH3+) lead-halide perovskite single crystal on picosecond time scales. The spectral and polarimetric measurements of the photon echo signal confirm the free excitonic origin of the excitation under study. Observed relatively long dephasing time, high exciton oscillator strength, and weakly pronounced excitation-induced dephasing make halide perovskites a promising media for applications.