If enough of their Lyman-limit continuum escapes, star-forming galaxies could be significant contributors to the cosmic background of ionizing photons. To investigate this possibility, we obtained the first deep imaging in the far-ultraviolet of 11 bright blue galaxies at intermediate redshift (1.1 < z < 1.4) with the Space Telescope Imaging Spectrograph Far-Ultraviolet Multianode Microchannel Array detector on the Hubble Space Telescope. No Lyman continuum emission was detected. Sensitive, model-independent, upper limits of typically less than 10-19 ergs cm-2 s-1 Å-1 were obtained for the ionizing flux escaping from these normal galaxies. This corresponds to lower limits on the observed ratio of 1500-700 Å flux of 150 up to 1000. On the basis of a wide range of stellar synthesis models, this suggests that less than 6%, down to less than 1%, of the available ionizing flux emitted by hot stars is escaping these galaxies. The magnitude of this spectral break at the Lyman limit confirms that the basic premise of "Lyman break" searches for galaxies at high redshift can also be applied at intermediate redshifts. This implies that the integrated contribution of galaxies to the UV cosmic background at z ~ 1.2 is less than 15% and may be less than 2%.