In recent years there have been numerous investigations of the helium shell-burning evolution of low-mass stars, and it was in such studies that Schwarzschild and Härm and Weigert independently discovered the thermal instability phenomenon. In the case of stars with hydrogen-rich envelopes, its reality has been amply confirmed. On the other hand, studies have also been made of the shell-burning in pure helium stars (many for comparison with the nuclei of planetary nebulae), and here the situation is far less clear. Some investigators have found the instability, while others have not. Paczyński has drawn attention to the fact that in all cases where thermal pulses have been reported for pure helium stars, the helium shell-source was treated as an abundance discontinuity, while in all cases where a detailed abundance profile was used, there was no evidence of pulses. He suggests therefore that the shells in pure helium stars are stable. We wish to report a calculation for a 0.8 ɱ⊙ pure helium star, with a detailed shell abundance profile, in which a single thermal pulse was encountered at the end of the shell-burning evolution.