High-resolution spectra of KrF (B-X) amplified spontaneous emission from various discharge-pumped and electron-beam-pumped KrF lasers have been analyzed. An underlying structured absorption spectrum has been discovered with a well-resolved peak at 248.91 nm. The absorption coefficient of this peak was found to vary in exact proportion to the peak laser gain coefficient but was independent of laser gas purity. We suggest that the absorption arises internally within the KrF molecule and is due to transitions from the B state to a higher-lying Rydberg state. This hypothesis was tested by simulating the absorption spectrum from KrF*(B) to a weakly repulsive state dissociating to Kr*(P-3(1))+F(P-2(3/2)). A good agreement was obtained between simulated and experimental absorption spectra.