We present a new pipeline for the efficient generation of synthetic observations of the extragalactic microwave sky, tailored to large ground-based CMB experiments such as the Simons Observatory, Advanced ACTPol, SPT-3G, and CMB-S4. Such simulated observations are a key technical challenge in cosmology because of the dynamic range and accuracy required. The first part of the pipeline generates a random cosmological realization in the form of a dark matter halo catalog and matter displacement field, as seen from a given position. The halo catalog and displacement field are modeled with ellipsoidal collapse dynamics and Lagrangian perturbation theory, respectively. In the second part, the cosmological realization is converted into a set of intensity maps over the range 10 - 10^3 GHz using models based on existing observations and hydrodynamical simulations. These maps include infrared emission from dusty star forming galaxies (CIB), Comptonization of CMB photons by hot gas in groups and clusters through the thermal Sunyaev-Zeldovich effect (tSZ), Doppler boosting by Thomson scattering of the CMB by bulk flows through the kinetic Sunyaev-Zeldovich effect (kSZ), and weak gravitational lensing of primary CMB anisotropies by the large-scale distribution of matter in the universe. After describing the pipeline and its implementation, we present the Websky maps, created from a realization of the cosmic web on our past light cone in the redshift interval 0<z<4.6 over the full-sky and a volume of ~(600 Gpc/h)^3 resolved with ~10^12 resolution elements. The Websky maps and halo catalog are publicly available at mocks.cita.utoronto.ca/websky.
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