We have made the first detections of the 88 mum [O III] line from galaxies in the early universe, detecting the line from the lensed active galactic nucleus (AGN)/starburst composite systems APM 08279+5255 at z = 3.911 and SMM J02399-0136 at z = 2.8076. The line is exceptionally bright from both systems, with apparent (lensed) luminosities ~1011 L sun. For APM 08279, the [O III] line flux can be modeled in a star formation paradigm, with the stellar radiation field dominated by stars with effective temperatures, T eff > 36,000 K, similar to the starburst found in M82. The model implies ~35% of the total far-IR luminosity of the system is generated by the starburst, with the remainder arising from dust heated by the AGN. The 88 mum line can also be generated in the narrow-line region of the AGN if gas densities are around a few 1000 cm-3. For SMM J02399, the [O III] line likely arises from H II regions formed by hot (T eff > 40,000 K) young stars in a massive starburst that dominates the far-IR luminosity of the system. The present work demonstrates the utility of the [O III] line for characterizing starbursts and AGN within galaxies in the early universe. These are the first detections of this astrophysically important line from galaxies beyond a redshift of 0.05.