In the numerical investigation of the evolution of a star of 1 Mo through the phases in which it contains a helium-burning shell as well as a hydrogen-burning shell, an unexpected type of thermal instability has been encountered. This instability is somewhat reminiscent of the helium flash even though degeneracy plays no role in the models considered. The existence of the instability has been made reasonably certain both by a physical analysis and by a direct mathematical derivation. The new instability appears to have the character of a thermal runaway in a non-degenerate shell containing a highly temperature-sensitive nuclear-energy source. Such a shell will be unstable only if it is sufficiently thin not to affect the over-all hydrostatic structure of the star noticeably. Under this condition the pressure within the shell cannot greatly increase during the thermal runaway, and hence cooling by an adiabatic expansion cannot stabilize the shell. Some speculations are presented regarding whether this instability could have substantial consequences for a star's evolution.