Chemical processes driven by nonthermal energy (e.g., visible light) are attractive for future approaches to energy conversion, synthesis, photocatalysis, and so forth. The growth of anisotropic metal nanostructures mediated by excitation of a localized surface plasmon resonance (LSPR) is a prototype example of such a reaction. Important aspects, notably the growth mechanism and a possible role of plasmonic "hot spots" within the metal nanostructures, remain poorly understood. Here, we use in situ electron microscopy to stimulate and image the plasmon-mediated growth of triangular Ag nanoprisms in solution. The quantification of the time-dependent evolution of the lateral size and thickness of the nanoprisms, enabled by nanometer-scale real-time microscopy in solution, shows a transition from an early stage of uniform Ag incorporation exclusively in the prism side facets to a size regime with accelerated growth in thickness. Differences in attachment rate at this advanced stage correlate with local plasmonic field enhancements, which allows determining the range over which charge carriers transferred from plasmonic hot spots can drive chemistry. Such data support the development of nonthermal chemical processes that depend on plasmonic light harvesting and the transfer of nonequilibrium charge carriers.