Intercellular communication via chemical signaling proceeds with both spatial and temporal components, but analytical tools, such as microfabricated electrodes, have been limited to just a few probes per cell. In this work, we use a nonphotobleaching fluorescent nanosensor array based on single-walled carbon nanotubes (SWCNTs) rendered selective to dopamine to study its release from PC12 neuroprogenitor cells at a resolution exceeding 20,000 sensors per cell. This allows the spatial and temporal dynamics of dopamine release, following K+ stimulation, to be measured at exceedingly high resolution. We observe localized, unlabeled release sites of dopamine spanning 100 ms to seconds that correlate with protrusions but not predominately the positive curvature associated with the tips of cellular protrusions as intuitively expected. The results illustrate how directionality of chemical signaling is shaped by membrane morphology, and highlight the advantages of nanosensor arrays that can provide high spatial and temporal resolution of chemical signaling.