We apply Support Vector Machines (SVMs)—a machine learning algorithm—to the task of classifying structures in the interstellar medium (ISM). As a case study, we present a position-position-velocity (PPV) data cube of 12 CO J = 3-2 emission toward G16.05-0.57, a supernova remnant that lies behind the M17 molecular cloud. Despite the fact that these two objects partially overlap in PPV space, the two structures can easily be distinguished by eye based on their distinct morphologies. The SVM algorithm is able to infer these morphological distinctions, and associate individual pixels with each object at >90% accuracy. This case study suggests that similar techniques may be applicable to classifying other structures in the ISM—a task that has thus far proven difficult to automate.