We present sensitive 850 μm imaging of the Cosmological Evolution Survey (COSMOS) field using 640 hr of new and archival observations taken with SCUBA-2 at the East Asian Observatory’s James Clerk Maxwell Telescope. The SCUBA-2 COSMOS survey (S2COSMOS) achieves a median noise level of σ 850μm = 1.2 mJy beam？1 over an area of 1.6 sq. degree (MAIN; Hubble Space Telescope/Advanced Camera for Surveys footprint), and σ 850μm = 1.7 mJy beam？1 over an additional 1 sq. degree of supplementary (SUPP) coverage. We present a catalog of 1020 and 127 sources detected at a significance level of >4σ and >4.3σ in the MAIN and SUPP regions, respectively, corresponding to a uniform 2% false-detection rate. We construct the single-dish 850 μm number counts at S 850 > 2 mJy and show that these S2COSMOS counts are in agreement with previous single-dish surveys, demonstrating that degree-scale fields are sufficient to overcome the effects of cosmic variance in the S 850 = 2─10 mJy population. To investigate the properties of the galaxies identified by S2COSMOS sources we measure the surface density of near-infrared-selected galaxies around their positions and identify an average excess of 2.0 ± 0.2 galaxies within a 13″ radius (∼100 kpc at z ∼ 2). The bulk of these galaxies represent near-infrared-selected submillimeter galaxies and/or spatially correlated sources and lie at a median photometric redshift of z = 2.0 ± 0.1. Finally, we perform a stacking analysis at submillimeter and far-infrared wavelengths of stellar-mass-selected galaxies (M ？ = 1010─1012 M ？) from z = 0─4, obtaining high-significance detections at 850 μm in all subsets (signal-to-noise ratio, S/N = 4─30), and investigate the relation between far-infrared luminosity, stellar mass, and the peak wavelength of the dust spectral energy distribution. The publication of this survey adds a new deep, uniform submillimeter layer to the wavelength coverage of this well-studied COSMOS field.