  We present the KMOS^3D survey, a new integral field survey of over 600
galaxies at 0.7<z<2.7 using KMOS at the Very Large Telescope (VLT). The KMOS^3D
survey utilizes synergies with multi-wavelength ground and space-based surveys
to trace the evolution of spatially-resolved kinematics and star formation from
a homogeneous sample over 5 Gyrs of cosmic history. Targets, drawn from a
mass-selected parent sample from the 3D-HST survey, cover the star
formation-stellar mass ($M_*$) and rest-frame $(U-V)-M_*$ planes uniformly. We
describe the selection of targets, the observations, and the data reduction. In
the first year of data we detect Halpha emission in 191
$M_*=3\times10^{9}-7\times10^{11}$ Msun galaxies at z=0.7-1.1 and z=1.9-2.7. In
the current sample 83% of the resolved galaxies are rotation-dominated,
determined from a continuous velocity gradient and $v_{rot}/\sigma>1$, implying
that the star-forming 'main sequence' (MS) is primarily composed of rotating
galaxies at both redshift regimes. When considering additional stricter
criteria, the Halpha kinematic maps indicate at least ~70% of the resolved
galaxies are disk-like systems. Our high-quality KMOS data confirm the elevated
velocity dispersions reported in previous IFS studies at z>0.7. For
rotation-dominated disks, the average intrinsic velocity dispersion decreases
by a factor of two from 50 km/s at z~2.3 to 25 km/s at z~0.9 while the
rotational velocities at the two redshifts are comparable. Combined with
existing results spanning z~0-3, disk velocity dispersions follow an
approximate (1+z) evolution that is consistent with the dependence of velocity
dispersion on gas fractions predicted by marginally-stable disk theory.
