The Spitzer Matching Survey of the Ultra-VISTA Deep Stripes (SMUVS) consists of deep 3.6 and 4.5 imaging of three Ultra-VISTA near-infrared survey stripes in the COSMOS field. SMUVS reaches point-source sensitivities of about 25.0 AB mag at both 3.6 and 4.5 microns with a significance of 4 sigma, accounting for both survey sensitivity and source confusion. To this limit, the SMUVS catalogs contain a total of ~350,000 sources, each of which is detected significantly in at least one IRAC band. Because of its uniform and high sensitivity, relatively large area coverage, and the wide array of ancillary data available in COSMOS, the SMUVS survey will be useful for a large number of cosmological investigations.