  The Carnegie Supernova Project (CSP) is designed to measure the luminosity
distance for Type Ia supernovae (SNe Ia) as a function of redshift, and to set
observational constraints on the dark energy contribution to the total energy
content of the Universe. The CSP differs from other projects to date in its
goal of providing an I-band {rest-frame} Hubble diagram. Here we present the
first results from near-infrared (NIR) observations obtained using the Magellan
Baade telescope for SNe Ia with 0.1 < z < 0.7. We combine these results with
those from the low-redshift CSP at z <0.1 (Folatelli et al. 2009). We present
light curves and an I-band Hubble diagram for this first sample of 35 SNe Ia
and we compare these data to 21 new SNe Ia at low redshift. These data support
the conclusion that the expansion of the Universe is accelerating. When
combined with independent results from baryon acoustic oscillations (Eisenstein
et al. 2005), these data yield Omega_m = 0.27 +/- 0.0 (statistical), and
Omega_DE = 0.76 +/- 0.13 (statistical) +/- 0.09 (systematic), for the matter
and dark energy densities, respectively. If we parameterize the data in terms
of an equation of state, w, assume a flat geometry, and combine with baryon
acoustic oscillations, we find that w = -1.05 +/- 0.13 (statistical) +/- 0.09
(systematic). The largest source of systematic uncertainty on w arises from
uncertainties in the photometric calibration, signaling the importance of
securing more accurate photometric calibrations for future supernova cosmology
programs. Finally, we conclude that either the dust affecting the luminosities
of SNe Ia has a different extinction law (R_V = 1.8) than that in the Milky Way
(where R_V = 3.1), or that there is an additional intrinsic color term with
luminosity for SNe Ia independent of the decline rate.
