Observations of material and cellular systems in response to time-varying chemical stimuli can aid the analysis of dynamic processes. We describe a microfluidic "chemical signal generator," a technique to apply continuously varying chemical concentration waveforms to arbitrary locations in a microfluidic channel through feedback control of the interface between parallel laminar (co-flowing) streams. As the flow rates of the streams are adjusted, the channel walls are exposed to a chemical environment that shifts between the individual streams. This approach can be used to probe the dynamic behavior of objects or substances adherent to the interior of the channel. To demonstrate the technique, we exposed live fibroblast cells to ionomycin, a membrane-permeable calcium ionophore, while assaying cytosolic calcium concentration. Through the manipulation of the laminar flow interface, we exposed the cells' endogenous calcium handling machinery to spatially-contained discrete and oscillatory intracellular disturbances, which were observed to elicit a regulatory response. The spatiotemporal precision of the generated signals opens avenues to previously unapproachable areas for potential investigation of cell signaling and material behavior.