In the last decade it has become increasingly clear that QSOs are probably not responsible for reionizing the universe at z > 6, making star formation the likely culprit. Consequently, there has been a concerted effort to measure the fraction of ionizing photons from star-forming galaxies that escape into the intergalactic medium. I will discuss our attempts to measure this "escape fraction" of ionizing photons in extremely deep (AB~29) far-UV images from the Hubble Space Telescope. We detect no ionizing flux in 21 star-forming galaxies at 1.2 < z < 1.5. For 18 galaxies, the limits imply relative escape fractions less than unity. Combined with a previous work at this redshift, the lack of detections implies a possible evolution in the escape fraction with redshift, though with some important caveats. I will conclude by outlining three ongoing HST programs to broaden and deepen the z~1 sample and to explain the high escape fractions exhibited in a few z~3 Lyman Break Galaxies.