We investigate the line-of-sight velocity oscillations in the sunspot NOAA 0051 during its disk transit. The data obtained in this study provide evidence for the existence of running umbral waves in the chromosphere. These waves have a period of 2.8 min and propagate from the sunspot center outward with the phase velocity of 45–60 km s^-1 with the line-of-sight velocity amplitude of about 2 km s^-1. In most cases the waves terminate rather abruptly on the umbra boundary and show no direct linkage with running penumbral waves. The spatial coherence of the waves at the umbra center is no more than 2″. At the photospheric level there are clearly pronounced periodic motions (T ~ 5 min) propagating from the inner penumbral boundary and from the superpenumbra to the lines of maximum Evershed velocity.