We present the KMOS{sup 3D} survey, a new integral field survey of over 600 galaxies at 0.7 < z < 2.7 using KMOS at the Very Large Telescope. The KMOS{sup 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 Gyr of cosmic history. Targets, drawn from a mass-selected parent sample from the 3D-HST survey, cover the star formation-stellar mass (M {sub *}) and rest-frame (U – V) – M {sub *} planes uniformly. We describe the selection of targets, the observations, and the data reduction. In the first-year of data we detect Hα emission in 191 M {sub *} = 3 × 10{sup 9}-7 × 10{sup 11} M {sub ☉} 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 {sub rot}/σ{sub 0} > 1, implying that the star-forming ''main sequence'' is primarily composed of rotating galaxies at both redshift regimes. When considering additional stricter criteria, the Hα kinematic maps indicate that at least ∼70% of the resolved galaxies are disk-like systems. Our high-quality KMOS data confirm the elevated velocity dispersions reported in previous integral field spectroscopy studies at z ≳ 0.7. For rotation-dominated disks, the average intrinsic velocity dispersion decreases by a factor of two from 50 km s{sup –1}at z ∼ 2.3 to 25 km s{sup –1}at z ∼ 0.9. Combined with existing results spanning z ∼ 0-3, we show that disk velocity dispersions follow an evolution that is consistent with the dependence of velocity dispersion on gas fractions predicted by marginally stable disk theory.