We have studied the electrochemically-induced pitting process on a Cu electrode in NaHCO3 solution using in-situ X-ray off-specular reflectivity measurements. The morphology and growth dynamics of the localized corrosion sites or pits were studied as the applied potential was varied from the cathodic region where the Cu surface is relatively free of oxide films to the anodic region where surface roughening occurs by general corrosion with concomitant formation of an oxide film. Quantitative analysis of the experimental results indicates that early pitting proceeds in favor of nucleation of pit clusters over individual pit growth. It was found that the lateral distribution of the pits is not random but exhibits a short-range order as evidenced by the appearance of a side peak in the transverse off-specular reflectivity. The position, height, and width of the peak was modeled to yield the average size, nearest-neighbor distance (within any one of the clusters), and over-all density of the pits averaged over the entire illuminated surface. In addition, measurements of the longitudinal off-specular reflectivity indicate a bimodal depth distribution for the pits, suggesting a "film breaking" type of pitting mechanism.