One major goal of biology is to provide a quantitative description of cellular physiology. This task is complicated by population effects, which perturb culture conditions and mask the behavior of the individual cell. To overcome these limitations, the construction and operation of a microfluidic bioreactor is presented. The new reactor concept guarantees constant environmental conditions and single cell resolution, thus it was named Envirostat (environment, constant). In the Envirostat, cells are contactless trapped by negative dielectrophoresis (nDEP) and cultivated in a constant medium flow. To control chip temperature, a Peltier device was constructed. Joule heating by nDEP was quantified with Rhodamine B in dependence of applied voltage, field mode, medium conductivity, and flow velocity. The integration of the Joule heating effect in the temperature control allowed setting and maintaining the cultivation temperature. For single cell cultivation of Saccharomyces cerevisiae, medium composition changes below 0.001% were estimated by computational fluid dynamic simulation. These changes were considered not to influence cell physiology. Finally, single S. cerevisiae cells were cultivated for more than four generations in the Envirostat, thus showing the applicability of the new reactor concept. The Envirostat facilitates single cell research and might simplify the investigation of hitherto difficult to access biological phenomena such as the true regulatory and physiological response to genetic and environmental perturbations.