Neutrophils are the most abundant type of white blood cells in the circulation, protecting the body against pathogens and responding early to inflammation. Although we understand how neutrophils respond to individual stimuli, we know less about how they prioritize between competing signals or respond to combinational signals. This situation is due in part to the lack of adequate experimental systems to provide signals in controlled spatial and temporal fashion. To address these limitations, we designed a platform for generating on-demand, competing chemical gradients and for monitoring neutrophil migration. On this platform, we implemented forty-eight assays generating independent gradients and employed synchronized valves to control the timing of these gradients. We observed faster activation of neutrophils in response to fMLP than to LTB4 and unveiled for the first time a potentiating effect for fMLP during migration towards LTB4. Our observations, enabled by the new tools, challenge the current paradigm of inhibitory competition between distinct chemoattractant gradients and suggest that human neutrophils are capable of complex integration of chemical signals in their environment.