jats:titleAbstract</jats:title> jats:pMolecular emission was imaged with ALMA from numerous components near and within bright Hjats:sub2</jats:sub>-emitting knots and absorbing dust globules in the Crab Nebula. These observations provide a critical test of how energetic photons and particles produced in a young supernova remnant interact with gas, cleanly differentiating between competing models. The four fields targeted show contrasting properties but within them, seventeen distinct molecular clouds are identified with CO emission; a few also show emission from HCOjats:sup+</jats:sup>, SiO, and/or SO. These observations are compared with Cloudy models of these knots. It has been suggested that the Crab filaments present an exotic environment in which Hjats:sub2</jats:sub> emission comes from a mostly neutral zone probably heated by cosmic rays produced in the supernova surrounding a cool core of molecular gas. Our model is consistent with the observed CO jats:italicJ</jats:italic> = 3 − 2 line strength. These molecular line emitting knots in the Crab Nebula present a novel phase of the ISM representative of many important astrophysical environments.</jats:p>