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We present a new chemical evolution model for the Galaxy that assumes two main infall episodes, for the formation of the halo-thick disk and thin disk, respectively. We do not try to take into account explicitly the evolution of the halo since our model is better suited for computing the evolution of the disk (thick plus thin), but we implicitly assume that the timescale for the formation of the halo was of the same order as the timescale for the formation of the thick disk. The formation of the thin disk is much longer than that of the thick disk, implying that the infalling gas forming the thin disk comes not only from the thick disk but mainly from the intergalactic medium. The timescale for the formation of the thin disk is assumed to be a function of Galactocentric distance, leading to an inside-out picture for the Galaxy's building. The model takes into account the most up-to-date nucleosynthesis prescriptions and adopts a threshold in the star formation process, which naturally produces a hiatus in the star formation rate at the end of the thick-disk phase, as suggested by recent observations. The model results are compared with an extended set of observational constraints both for the solar neighborhood and for the whole disk. Among these constraints, the tightest is the metallicity distribution of the G-dwarf stars, for which new data are now available. Our model fits these new data very well. The model also predicts the evolution of the gas mass, the star formation rate, the supernova rates, and the abundances of 16 chemical elements as functions of time and Galactocentric distance. We show that, in order to reproduce most of these constraints, a timescale of <=1 Gyr for the (halo) thick disk and of 8 Gyr for the thin disk's formation in the solar vicinity are required. We predict that the radial abundance gradients in the inner regions of the disk (R < 1 Rsun) are steeper than in the outer regions, a result confirmed by recent abundance determinations, and that the inner gradients steepen during the Galactic lifetime. The importance and the advantages of assuming a threshold gas density for the onset of the star formation process are discussed.