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For decades we have known that the Sun lies within the Local Bubble, a cavity of low-density, high-temperature plasma surrounded by a shell of cold, neutral gas and dust. However, the precise shape and extent of this shell, the impetus and timescale for its formation, and its relationship to nearby star formation have remained uncertain, largely due to low-resolution models of the local interstellar medium. Leveraging new spatial and dynamical constraints from the Gaia space mission, here we report an analysis of the 3D positions, shapes, and motions of dense gas and young stars within 200 pc of the Sun. We find that nearly all the star-forming complexes in the solar vicinity lie on the surface of the Local Bubble and that their young stars show outward expansion mainly perpendicular to the bubble's surface. Tracebacks of these young stars' motions support a scenario where the origin of the Local Bubble was a burst of stellar birth and then death (supernovae) taking place near the bubble's center beginning 14 Myr ago. The expansion of the Local Bubble created by the supernovae swept up the ambient interstellar medium into an extended shell that has now fragmented and collapsed into the most prominent nearby molecular clouds, in turn providing robust observational support for the theory of supernova-driven star formation.