Galaxy rotation curves provide fundamental measurements of the baryonic and dark matter distributions in galaxies. The kinematic studies of galaxies in the local Universe, showing that the enclosed dynamical mass of galaxies rises far beyond the optical radius, remains one of the cornerstones for the evidence for dark matter. There is less direct evidence for the same dark-matter dominance at high redshift, with recent studies suggesting that dark matter contribution within galaxies may be much lower. To measure the shapes of rotation curves of highredshift galaxies, we are undertaking the KMOS Ultradeep Rotational Velocity Survey (KURVS) which is deep (~120h per galaxy) study of z~1.5 main-sequence galaxies. These data, which are a factor ~10x deeper than previously undertaken, measure individual Hα rotation curves out to ~15kpc. Here, I will show how we are decomposing the rotation curves in to the speeds of stars, gas and dark matter, and discuss the implications from our study.