The Milky Way nuclear star cluster (MW NSC) has been used as a template to understand the origin and evolution of galactic nuclei and the interaction of nuclear star clusters with supermassive black holes. It is the only nuclear star cluster with a supermassive black hole where we can resolve individual stars to measure their kinematics and metal abundance to reconstruct its formation history. Here, we present results of the first chemo-dynamical model of the inner 1 pc of the MW NSC using metallicity and radial velocity data from the KMOS spectrograph on the Very Large Telescope. We find evidence for two kinematically and chemically distinct components in this region. The majority of the stars belong to a previously known super-solar metallicity component with a rotation axis perpendicular to the Galactic plane. However, we identify a new kinematically distinct sub-solar metallicity component which contains about 7% of the stars and appears to be rotating faster than the main component with a rotation axis that may be misaligned. This second component may be evidence for an infalling star cluster or remnants of a dwarf galaxy, merging with the MW NSC. These measurements show that the combination of chemical abundances with kinematics is a promising method to directly study the MW NSCs origin and evolution.