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We present PHIBSS, the IRAM Plateau de Bure high-z blue sequence CO 3-2 survey of the molecular gas properties in massive, main-sequence star-forming galaxies (SFGs) near the cosmic star formation peak. PHIBSS provides 52 CO detections in two redshift slices at z ~ 1.2 and 2.2, with log(M"(M☉)) ⩾ 10.4 and log(SFR(M☉/yr)) ⩾ 1.5. Including a correction for the incomplete coverage of the M"-SFR plane, and adopting a "Galactic" value for the CO-H2 conversion factor, we infer average gas fractions of ~0.33 at z ~ 1.2 and ~0.47 at z ~ 2.2. Gas fractions drop with stellar mass, in agreement with cosmological simulations including strong star formation feedback. Most of the z ~ 1-3 SFGs are rotationally supported turbulent disks. The sizes of CO and UV/optical emission are comparable. The molecular-gas-star-formation relation for the z = 1-3 SFGs is near-linear, with a ~0.7 Gyr gas depletion timescale; changes in depletion time are only a secondary effect. Since this timescale is much less than the Hubble time in all SFGs between z ~ 0 and 2, fresh gas must be supplied with a fairly high duty cycle over several billion years. At given z and M", gas fractions correlate strongly with the specific star formation rate (sSFR). The variation of sSFR between z ~ 0 and 3 is mainly controlled by the fraction of baryonic mass that resides in cold gas. [ABSTRACT FROM AUTHOR]