Chimaera (Holocephali) are cartilaginous fishes with flexible operculi rather than external gill slits, suggesting ventilation occurs in a manner different from other fishes. We examined holocephalan ventilation morphology, behavior, and performance by anatomical investigations, high-speed video, and in vivo pressure measurements from the buccal and parabranchial cranial cavities in Hydrolagus colliei and Callorhinchus callorynchus. Ventilatory modes ranged from quiet resting breathing to rapid “active” breathing, yet external cranial movements—excepting the passive movement of the opercular flap—were always extremely subtle, and pressures generated were one to two orders of magnitude lower than those of other fishes. To explain ventilation with such minimal pressure generation and cranial motion, we propose an “accordion” model, whereby rostrocaudal movement of the visceral arches drives pressure differentials, albeit with little lateral or ventral movement. Chimaeroids have comparatively large oropharyngeal cavities, which can move fluid with a smaller linear dimension change than the comparatively smaller cavities of other fishes. Orobranchial pressures are often less than parabranchial pressures, suggesting flow in the “wrong” direction; however, the long gill curtains of chimaeroids may passively restrict backflow. We suggest that constraints on holocephalan jaw and hyoid movements were compensated for evolutionarily by novel visceral arch mechanics and kinematics. J. Morphol., 2012. © 2011 Wiley Periodicals, Inc.