We report spectroscopic and imaging observations of rotational transitions of cold CO and SiO in the ejecta of SN1987A, the first such emission detected in a supernova remnant. In addition to line luminosities for the CO J = 1-0, 2-1, 6-5, and 7-6 transitions, we present upper limits for all other transitions up to J = 13-12, collectively measured from the Atacama Large Millimeter Array, the Atacama Pathfinder EXperiment, and the Herschel Spectral and Photometric Imaging REceiver. Simple models show the lines are emitted from at least 0.01 M ⊙ of CO at a temperature >14 K, confined within at most 35% of a spherical volume expanding at ∼2000 km s-1. Moreover, we locate the emission within 1′′ of the central debris. These observations, along with a partial observation of SiO, confirm the presence of cold molecular gas within supernova remnants and provide insight into the physical conditions and chemical processes in the ejecta. Furthermore, we demonstrate the powerful new window into supernova ejecta offered by submillimeter observations. © 2013. The American Astronomical Society. All rights reserved.