The nEXO experiment aims to discover neutrinoless double beta decay of xenon 136, with a half-life sensitivity goal of greater than 10^28 years. Compared to using long cables to transmit signals outside of the detector, mounting amplification and digitization circuitry directly on detector submodules reduces noise, system complexity, and improves measurement fidelity. A cryogenic application specific integrated circuit (ASIC) called CRYO ASIC has been designed by SLAC and fabricated for direct readout of the nEXO ionization-charge detection modules. A prototype nEXO charge-readout module with an ASIC attached has been operated in a liquid xenon time projection chamber; the full integrated assembly of parts, xenon compatible cabling, and charge-measurement performance of the module will be discussed.