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We report experimental results for chip-to-chip data communications on a superconducting Multi-Chip-Module (MCM) using a novel fabrication technique. The MCM was produced using a non-conductive adhesive to bond a 5-mm times 5-mm test chip to a 1-cm times 1-cm carrier. To our knowledge, this is the first time this technique was used for MCM assembly at cryogenic temperatures. The module demonstrated superior mechanical stability and protection from its environment during thermal cycling. The MCM also retained its electrical properties after multiple thermal cycling from room temperature to 4 K. We designed test circuits including various digital test benches, as well as analog test structures for bump characteristics. The superconducting circuitry successfully passed single-flux quanta at rates exceeding 50 Gbps. We measured error rates lower than 5 times 10-14 at 36 Gbps using 100-micrometer- diameter In-Sn solder bumps, and lower than 6 times 10-14 at 57 Gbps using 30-micrometer-diameter solder bumps.