In this letter, we present for the first time evidence in the BATSE data for a prompt high-energy (25-300 keV) afterglow component from a Gamma-Ray Burst (GRB), GRB980923. The event ranks third highest in fluence (>25 keV) in the BATSE catalog and consists of a period of rapid variability lasting about 40 s followed by a smooth power law emission tail lasting about 400 s beyond the trigger time. An abrupt change in spectral shape is found when the tail becomes noticeable. Our analysis reveals that the spectral evolution in the tail of the burst mimics that of a cooling synchrotron spectrum, similar to the spectral evolution of the low-energy afterglows for GRBS. This evidence for a separate emission component is consistent with the internal-external shock scenario in the relativistic fireball picture. In particular, it illustrates that the external shocks can be generated during the primary gamma-ray emission phase, as in the case of GRB990123.