A total absorption spectrometer, dedicated to the study of very short-lived atomic species, has been built and installed at the CERN/ISOLDE mass separator. The  decay of the neutron-deficient 74 Kr nucleus has been studied using this new device. The Gamow-Teller strength distribution has been observed over most of the Q EC window, and a total strength of 0.69͑3͒ g A 2 /4 has been measured for states with excitation energy below 3 MeV. Shape mixing in the 74 Kr ground state is inferred from a comparison of the experimental strength distribution with self-consistent, deformed, quasiparticle-random-phase-approximation calculations.