Using data from the Fermi Large Area Telescope (LAT), we report the first clear gamma-ray measurement of a delay between flares from the gravitationally lensed images of a blazar. The delay was detected in B0218+357, a known double-image lensed system, during a period of enhanced gamma-ray activity with peak fluxes consistently observed to reach >20-50 times its previous average flux. An auto-correlation function analysis identified a delay in the gamma-ray data of 11.46 +/- 0.16 days (1 sigma) that is ~1 day greater than previous radio measurements. Considering that it is beyond the capabilities of the LAT to spatially resolve the two images, we nevertheless decomposed individual sequences of superposing gamma-ray flares/delayed emissions. In three such ~8-10 day-long sequences within a ~4-month span, considering confusion due to overlapping flaring emission and flux measurement uncertainties, we found flux ratios consistent with ~1, thus systematically smaller than those from radio observations. During the first, best-defined flare, the delayed emission was detailed with a Fermi pointing, and we observed flux doubling timescales of ~3-6 hrs implying as well extremely compact gamma-ray emitting regions.Read less <