Compact starburst galaxies are thought to include many or most of the galaxies from which substantial Lyman continuum emission can escape into the intergalactic medium. Li and Malkan (2018) used SDSS photometry to find a population of such starburst galaxies at z~0.5. They were discovered by their extremely strong [OIII]4959+5007 emission lines, which produce a clearly detectable excess brightness in the i bandpass, compared with surrounding filters. We therefore used the HST/COS spectrograph to observe two of the newly discovered i-band excess galaxies around their Lyman limits. One has strongly detected continuum below its Lyman limit, corresponding to a relative escape fraction of ionizing photons of 20+/-2%. The other, which is less compact in UV imaging, has a 2-sigma upper limit to its Lyman escape fraction of <5%. Before the UV spectroscopy, the existing data could not distinguish these two galaxies. Although a sample of two is hardly sufficient for statistical analysis, it shows the possibility that some fraction of these strong [OIII] emitters as a class have ionizing photons escaping. The differences might be determined by the luck of our particular viewing geometry. Obtaining the HST spectroscopy, revealed that the Lyman-continuum emitting galaxy differs in having no central absorption in its prominent Ly{alpha} emission line profile. The other target, with no escaping Lyman continuum, shows the more common double-peaked Ly{alpha} emission.