Past X-ray observations of the nearby luminous quasar PDS 456 (at $z=0.184$) have revealed a wide angle accretion disk wind (Nardini et al. 2015), with an outflow velocity of $sim-0.25c$. Here we unveil a new, relativistic component of the wind through hard X-ray observations with NuSTAR and XMM-Newton, obtained in March 2017 when the quasar was in a low flux state. This very fast wind component, with an outflow velocity of $-0.46pm0.02c$, is detected in the iron K band, in addition to the $-0.25c$ wind zone. The relativistic component may arise from the innermost disk wind, launched from close to the black hole at radius of $sim10$ gravitational radii. The opacity of the fast wind also increases during a possible obscuration event lasting for 50 ks. We suggest that the very fast wind may only be apparent during the lowest X-ray flux states of PDS 456, becoming overly ionized as the luminosity increases. Overall, the total wind power may even approach the Eddington value.