We present evidence for very high gas fractions and extended molecular gas reservoirs in normal, near-infrared-selected (BzK) galaxies at z ∼ 1.5. Our results are based on multi-configuration CO2–1 observations obtained at the IRAM Plateau de Bure Interferometer. All six star-forming galaxies observed were detected at high significance. High spatial resolution observations resolve the CO emission in four of them, implying sizes of the gas reservoirs of order of 6–11 kpc and suggesting the presence of ordered rotation. The galaxies have UV morphologies consistent with clumpy, unstable disks, and UV sizes that are consistent with those measured in CO. The star formation efficiencies are homogeneously low within the sample and similar to those of local spirals—the resulting gas depletion times are ∼0.5 Gyr, much higher than what is seen in high-z submillimeter galaxies and quasars. The CO luminosities can be predicted to within 0.15 dex from the observed star formation rates (SFRs) and stellar masses, implying a tight correlation of the gas mass with these quantities. We use new dynamical models of clumpy disk galaxies to derive dynamical masses for our sample. These models are able to reproduce the peculiar spectral line shapes of the CO emission. After accounting for the stellar and dark matter masses, we derive molecular gas reservoirs with masses of (0.4–1.2)×1011 M☉. The implied conversion (CO luminosity-to-gas mass) factor is very high: αCO = 3.6 ± 0.8, consistent with a Galactic conversion factor but 4 times higher than that of local ultra-luminous IR galaxies that is typically used for high-redshift objects. The gas mass in these galaxies is comparable to or larger than the stellar mass, and the gas accounts for an impressive 50%–65% of the baryons within the galaxies' half-light radii. We are thus witnessing truly gas-dominated galaxies at z ∼ 1.5, a finding that explains the high specific SFRs observed for z > 1 galaxies. The BzK galaxies can be viewed as scaled-up versions of local disk galaxies, with low-efficiency star formation taking place inside extended, low-excitation gas disks. These galaxies are markedly different than local ULIRGs and high-z submillimeter galaxies and quasars, where higher excitation and more compact gas is found