Bacteria and yeast frequently exist as populations capable of reaching extremely high cell densities. With conventional culturing techniques, however, cell proliferation and ultimate density are limited by depletion of nutrients and accumulation of metabolites in the medium. Here we describe design and operation of microfabricated elastomer chips, in which chemostatic conditions are maintained for bacterial and yeast colonies growing in an array of shallow microscopic chambers. Walls of the chambers are impassable for the cells, but allow diffusion of chemicals. Thus, the chemical contents of the chambers are maintained virtually identical to those of the nearby channels with continuous flowthrough of a dynamically defined medium. We demonstrate growth of cell cultures to densely packed ensembles that proceeds exponentially in a temperature-dependent fashion, and we use the devices to monitor colony growth from a single cell and to analyze the cell response to an exogenously added autoinducer.