Our Sun lies within 300 parsecs of the 2.7-kiloparsecs-long sinusoidal chain of dense gas clouds known as the Radcliffe Wave1. The structure's wave-like shape was discovered using three-dimensional dust mapping, but initial kinematic searches for oscillatory motion were inconclusive2-7. Here we present evidence that the Radcliffe Wave is oscillating through the Galactic plane while also drifting radially away from the Galactic Centre. We use measurements of line-of-sight velocity8 for 12CO and three-dimensional velocities of young stellar clusters to show that the most massive star-forming regions spatially associated with the Radcliffe Wave (including Orion, Cepheus, North America and Cygnus X) move as though they are part of an oscillating wave driven by the gravitational acceleration of the Galactic potential. By treating the Radcliffe Wave as a coherently oscillating structure, we can derive its motion independently of the local Galactic mass distribution, and directly measure local properties of the Galactic potential as well as the Sun's vertical oscillation period. In addition, the measured drift of the Radcliffe Wave radially outwards from the Galactic Centre suggests that the cluster whose supernovae ultimately created today's expanding Local Bubble9 may have been born in the Radcliffe Wave.
