The longitudinal and transverse relaxation times for a transition between hyperfine sublevels of the lower electronic states of the 4I15/2 and 4I9/2 multiplets of 167Er3+ ions in 7LiYF4 crystals have been determined for the first time using two-pulse and stimulated photon echo measurements in zero magnetic field at a temperature of 4 K. The decay of the photon echo signal has been shown to be modulated, which is tentatively attributed to the superhyperfine interaction of the 167Er3+ ions with their 19F− nearest neighbours. The contributions of various types of interaction to the ultranarrow linewidth (~24 MHz) of the transition in question are discussed. Our results demonstrate that this optical transition of the 167Er3+ ion in 7LiYF4 crystals is potentially attractive for use in Raman quantum memory schemes.