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We present the survey design, implementation, and outlook for COSMOS-Web, a 255 hour treasury program conducted by the James Webb Space Telescope in its first cycle of observations. COSMOS-Web is a contiguous 0.54 deg$^2$ NIRCam imaging survey in four filters (F115W, F150W, F277W, and F444W) that will reach 5$σ$ point source depths ranging $\sim$27.5-28.2 magnitudes. In parallel, we will obtain 0.19 deg$^2$ of MIRI imaging in one filter (F770W) reaching 5$σ$ point source depths of $\sim$25.3-26.0 magnitudes. COSMOS-Web will build on the rich heritage of multiwavelength observations and data products available in the COSMOS field. The design of COSMOS-Web is motivated by three primary science goals: (1) to discover thousands of galaxies in the Epoch of Reionization ($6<z<11$) and map reionization's spatial distribution, environments, and drivers on scales sufficiently large to mitigate cosmic variance, (2) to identify hundreds of rare quiescent galaxies at $z>4$ and place constraints on the formation of the Universe's most massive galaxies ($M_\star>10^{10}$\,M$_\odot$), and (3) directly measure the evolution of the stellar mass to halo mass relation using weak gravitational lensing out to $z\sim2.5$ and measure its variance with galaxies' star formation histories and morphologies. In addition, we anticipate COSMOS-Web's legacy value to reach far beyond these scientific goals, touching many other areas of astrophysics, such as the identification of the first direct collapse black hole candidates, ultracool sub-dwarf stars in the Galactic halo, and possibly the identification of $z>10$ pair-instability supernovae. In this paper we provide an overview of the survey's key measurements, specifications, goals, and prospects for new discovery.