Organs-on-Chips (OoCs) are testing platforms for the pharmaceutical, cosmetic, and chemical industries. They are composed of miniaturized organ tissues (so-called organ modules) that are connected via a microfluidic channel network and, by this, emulate human or other animal physiology on a miniaturized chip. The design of those chips, however, requires a sophisticated orchestration of numerous aspects, such as the size of organ modules, the required shear stress on membranes, the dimensions and geometry of channels, pump pressures, etc. Mastering all this constitutes a non-trivial design task for which, unfortunately, no automatic support exists yet. In this work, we propose a first design automation solution for OoCs. To this end, we review the respective design steps and formalize a corresponding design specification from it. Based on that, we then propose an automatic method which solutions that generates a design of the desired device. Evaluations (inspired by real-world use cases and confirmed by CFD simulations) demonstrate the applicability and validity of the proposed approach.