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We present K-band spectra of rest-frame optical emission lines for 24star-forming galaxies at z~3.2-3.7 using MOSFIRE on the Keck 1 telescope.Strong rest-frame optical [O III] and Hbeta emission lines were detected in 18LBGs. The median flux ratio of [O III]5007 to Hbeta is 5.1+/-0.5, a factor of5-10x higher than in local galaxies with similar stellar masses. The observedHbeta luminosities are in good agreement with expectations from the estimatedstar-formation rates, and none of our sources are detected in deep X-raystacks, ruling out significant contamination by active galactic nuclei.Combining our sample with a variety of LBGs from the literature, including 49galaxies selected in a very similar manner, we find a high median ratio of[OIII]/Hbeta = 4.8+0.8-1.7. This high ratio seems to be an ubiquitous featureof z~3-4 LBGs, very different from typical local star-forming galaxies atsimilar stellar masses. The only comparable systems at z~0 are those withsimilarly high specific star-formation rates, though ~5x lower stellar masses.High specific star-formation rates either result in a much higher ionizationparameter or other unusual conditions for the interstellar medium, which resultin a much higher [OIII]/Hbeta line ratio. This implies a strong relationbetween a global property of a galaxy, the specific star-formation rate, andthe local conditions of ISM in star-forming regions.

Rest-Frame Optical Emission Lines in z~3.5 Lyman Break selected Galaxies: The Ubiquity of Unusually High [OIII]/Hbeta Ratios at 2 Gyr