  The KMOS Redshift One Spectroscopic Survey (KROSS) is an ESO guaranteed time
survey of 795 typical star-forming galaxies in the redshift range z=0.8-1.0
with the KMOS instrument on the VLT. In this paper we present resolved
kinematics and star formation rates for 584 z~1 galaxies. This constitutes the
largest near-infrared Integral Field Unit survey of galaxies at z~1 to date. We
demonstrate the success of our selection criteria with 90% of our targets found
to be Halpha emitters, of which 81% are spatially resolved. The fraction of the
resolved KROSS sample with dynamics dominated by ordered rotation is found to
be 83$\pm$5%. However, when compared with local samples these are turbulent
discs with high gas to baryonic mass fractions, ~35%, and the majority are
consistent with being marginally unstable (Toomre Q~1). There is no strong
correlation between galaxy averaged velocity dispersion and the total star
formation rate, suggesting that feedback from star formation is not the origin
of the elevated turbulence. We postulate that it is the ubiquity of high
(likely molecular) gas fractions and the associated gravitational instabilities
that drive the elevated star-formation rates in these typical z~1 galaxies,
leading to the ten-fold enhanced star-formation rate density. Finally, by
comparing the gas masses obtained from inverting the star-formation law with
the dynamical and stellar masses, we infer an average dark matter to total mass
fraction within 2.2$r_e$ (9.5kpc) of 65$\pm$12%, in agreement with the results
from hydrodynamic simulations of galaxy formation.
