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We present Keck/MOSFIRE spectra of the diagnostic nebular emission lines[OIII]5007,4959, [OII]3727, and H-beta for a sample of 15 redshift z=3.1-3.7Ly-alpha emitters (LAEs) and Lyman break galaxies (LBGs). In conjunction withspectra from other surveys, we confirm earlier indications that LAEs have amuch higher [OIII]/[OII] line ratio than is seen in similar redshift LBGs. Bycomparing their distributions on a [OIII]/[OII] versus R23 diagram, wedemonstrate that this difference cannot arise solely because of their lowermetallicities but most likely is due to a harder ionizing spectrum. Usingmeasures of H-beta and recombination theory, we demonstrate, for a subset ofour LAEs, that xi_ion - the number of Lyman continuum photons per UV luminosity- is indeed 0.2-0.5 dex larger than for typical LBGs at similar redshifts.Using photoionization models we estimate the effect this would have on both[OIII]/[OII] and R23 and conclude such a hard spectrum can only partiallyexplain such intense line emission. The additional possibility is that such alarge [OIII]/[OII] ratio is in part due to density rather than ionization boundnebular regions, which would imply a high escape fraction of ionizing photons.We discuss how further observations could confirm this possibility. ClearlyLAEs with intense [OIII] emission represent a promising analog of those z>7sources with similarly strong lines which are thought to be an importantcontributor to cosmic reionization.

A Hard Ionizing Spectrum in z=3-4 Ly-alpha Emitters with Intense [OIII] Emission: Analogs of Galaxies in the Reionization Era?