Enceladus presents an excellent opportunity to detect organic molecules that are relevant for habitability as well as bioorganic molecules that provide evidence for extraterrestrial life because Enceladus' plume is composed of material from the subsurface ocean that has a high habitability potential and significant organic content. A primary challenge is to send instruments to Enceladus that can efficiently sample organic molecules in the plume and analyze for the most relevant molecules with the necessary detection limits. To this end, we present the scientific feasibility and engineering design of the Enceladus Organic Analyzer (EOA) that uses a microfluidic capillary electrophoresis system to provide sensitive detection of a wide range of relevant organic molecules, including amines, amino acids, and carboxylic acids, with ppm plume-detection limits (100 pM limits of detection). Importantly, the design of a capture plate that effectively gathers plume ice particles at encounter velocities from 200 m/s to 5 km/s is described, and the ice particle impact is modeled to demonstrate that material will be efficiently captured without organic decomposition. While the EOA can also operate on a landed mission, the relative technical ease of a fly-by mission to Enceladus, the possibility to nondestructively capture pristine samples from deep within the Enceladus ocean, plus the high sensitivity of the EOA instrument for molecules of bioorganic relevance for life detection argue for the inclusion of EOA on Enceladus missions. Key Words: Lab-on-a-chip-Organic biomarkers-Life detection-Planetary exploration. Astrobiology 17, 902-912.