For the past 150 years, the prevailing view of the local Interstellar Medium (ISM) was based on a peculiarity known as the Goulds Belt, an expanding ring of young stars, gas, and dust, tilted about 20$^circ$ to the Galactic plane. Still, the physical relation between local gas clouds has remained practically unknown because the distance accuracy to clouds is of the same order or larger than their sizes. With the advent of large photometric surveys and the Gaia satellite astrometric survey this situation has changed. Here we report the 3-D structure of all local cloud complexes. We find a narrow and coherent 2.7 kpc arrangement of dense gas in the Solar neighborhood that contains many of the clouds thought to be associated with the Gould Belt. This finding is inconsistent with the notion that these clouds are part of a ring, disputing the Gould Belt model. The new structure comprises the majority of nearby star-forming regions, has an aspect ratio of about 1:20, and contains about 3 million solar masses of gas. Remarkably, the new structure appears to be undulating and its 3-D distribution is well described by a damped sinusoidal wave on the plane of the Milky Way, with an average period of about 2 kpc and a maximum amplitude of about 160 pc. Our results represent a first step in the revision of the local gas distribution and Galactic structure and offer a new, broader context to studies on the transformation of molecular gas into stars.
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