Scanning electrochemical cell microscopy (SECCM) has been applied for nanoscale (electro)activity mapping in a range of electrochemical systems but so far has almost exclusively been performed in controlled-potential (amperometric/voltammetric) modes. Herein, we consider the use of SECCM operated in a controlled-current (galvanostatic or chronopotentiometric) mode, to synchronously obtain spatially resolved electrode potential (i.e., electrochemical activity) and topographical "maps". This technique is first applied, as proof of concept, to study the electrochemically reversible [Ru(NH3)6]3+/2+ electron transfer process at a glassy carbon electrode surface, where the experimental data are in good agreement with well-established chronopotentiometric theory under quasi-radial diffusion conditions. The [Ru(NH3)6]3+/2+ process has also been imaged at "aged" highly ordered pyrolytic graphite (HOPG), where apparently enhanced electrochemical activity is measured at the edge plane relative to the basal plane surface, consistent with potentiostatic measurements. Finally, chronopotentiometric SECCM has been employed to benchmark a promising electrocatalytic system, the hydrogen evolution reaction (HER) at molybdenum disulfide (MoS2), where higher electrocatalytic activity (i.e., lower overpotential at a current density of 2 mA cm-2) is observed at the edge plane compared to the basal plane surface. These results are in excellent agreement with previous controlled-potential SECCM studies, confirming the viability of the technique and thereby opening up new possibilities for the use of chronopotentiometric methods for quantitative electroanalysis at the nanoscale, with promising applications in energy storage (battery) studies, electrocatalyst benchmarking, and corrosion research.