Two key areas of emphasis in contemporary experimental exoplanet science are the detailed characterization of transiting terrestrial planets, and the search for Earth analog planets to be targeted by future imaging missions. Both of these pursuits are dependent on an order-of-magnitude improvement in the measurement of stellar radial velocities (RV), setting a requirement on single-measurement instrumental uncertainty of order 10 cm/s. Achieving such extraordinary precision on a high-resolution spectrometer requires thermo-mechanically stabilizing the instrument to unprecedented levels. Here, we describe the Environment Control System (ECS) of the NEID Spectrometer, which will be commissioned on the 3.5 m WIYN Telescope at Kitt Peak National Observatory in 2019, and has a performance specification of on-sky RV precision < 50 cm/s. Because NEIDs optical table and mounts are made from aluminum, which has a high coefficient of thermal expansion, sub-milliKelvin temperature control is especially critical. NEID inherits its ECS from that of the Habitable-zone Planet Finder (HPF), but with modifications for improved performance and operation near room temperature. Our full-system stability test shows the NEID system exceeds the already impressive performance of HPF, maintaining vacuum pressures below $10^{-6}$ Torr and an RMS temperature stability better than 0.4 mK over 30 days. Our ECS design is fully open-source; the design of our temperature-controlled vacuum chamber has already been made public, and here we release the electrical schematics for our custom Temperature Monitoring and Control (TMC) system.