We present observations of the CO[3-2] emission towards two massive and infrared luminous Lyman Break Galaxies at z = 3.21 and z = 2.92, using the IRAM Plateau de Bure Interferometer, placing first constraints on the molecular gas masses (Mgas) of non-lensed LBGs. Their overall properties are consistent with those of typical (Main-Sequence) galaxies at their redshifts, with specific star formation rates ~1.6 and ~2.2 Gyr^(-1), despite their large infrared luminosities L_IR ~2-3 x 10^12 Lsun derived from Herschel. With one plausible CO detection (spurious detection probability of 10^(-3)) and one upper limit, we investigate the evolution of the molecular gas-to-stellar mass ratio (Mgas/M*) with redshift. Our data suggest that the steep evolution of Mgas/M* of normal galaxies up to z~2 is followed by a flattening at higher redshifts, providing supporting evidence for the existence of a plateau in the evolution of the specific star formation rate at z > 2.5.
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