This paper introduces a chain-driven, sandwich-legged mid-size quadruped robot designed as an accessible research platform. The design prioritizes enhanced locomotion, improved actuation reliability and safety, and simplified, cost-effective manufacturing. Locomotion performance is improved through a sandwiched leg architecture and dual-motor configuration, reducing leg inertia for agile motion. Reliability and safety are enhanced using robust cable strain reliefs, motor heat sinks for thermal management, and mechanical limits to restrict leg motion. The design incorporates quasi-direct-drive (QDD) actuators and low-cost fabrication methods such as laser cutting and 3D printing for rapid prototyping. The $25\,\mathrm{kg}$ robot is built under \$8000, providing an affordable quadruped research platform. Experiments demonstrate trot and crawl gaits on flat terrain and slopes. We also open-source the mechanical designs. VIDEO: https://youtu.be/ygSMCPcFnP8?feature=shared CADs: https://github.com/singhaman1750/stoch3-design.git