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 beta decay of the neutron-deficient Kr-74 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 0.69(3) g(A)(2)/4pi has been measured for states with excitation energy below 3 MeV. Shape mixing in the Kr-74 ground state is inferred from a comparison of the experimental strength distribution with self-consistent, deformed, quasiparticle-random-phase-approximation calculations.