Embryonic development of the spinal cord proceeds through a carefully orchestrated temporal and spatial sequence of chemical cues to provide precise patterning of adult cell types. Recreating this complex microenvironment in a standard cell culture dish is difficult, if not impossible. In this paper, a microfluidic device is used to recapitulate, in vitro, the graded patterning events which occur during early spinal cord development. The microdevice design is developed using COMSOL modeling, with which the spatiotemporal profiles of multiple, diffusible morphogens are simulated. Four independently addressed source/sinks are employed to generate two overlapping orthogonal gradients within a cell culture chamber, mimicking the dorsoventral and anteroposterior axes of the developing embryo. Mouse embryonic stem cells are directed therein to differentiate into motor neurons in a spatially organized manner, reminiscent of a neural tube.