For over fifty years astronomers sought inconclusively to confirm Albert Einstein's prediction of a "gravitational red shift" by studies of solar and stellar spectra. Although it was expected by the 1950s that the combination of atomic clocks with vehicles sent into space would finally enable a conclusive test, the development of precise examples of the resonant absorption of gamma rays between nuclei bound in solids, discovered by Rudolf Mössbauer in 1958, provided a basis for an experiment within an earthbound laboratory. I describe the trials and tribulations of making the necessary extension of the phenomenon, including the discovery of the unanticipated effect of temperature as causing relativistic time dilation, that led to a successful confirmation in March of 1960 of a shift amounting to only 2.5 2 10m15 to less than a 10% uncertainty.