Gravitational lensing provides a unique probe of the inner 10-1000 pc of distant galaxies (z ~ 0.2-1). Theoretical studies have predicted that each strong lens system should have a faint image near the center of the lens galaxy, which should, in principle, be visible in radio lenses but has never been detected. We study the predicted "core" images using models derived from the stellar distributions in nearby early-type galaxies. We find that realistic lens galaxies produce a remarkably wide range of core images, with magnifications spanning some 6 orders of magnitude. More concentrated galaxies produce fainter core images, although not with any model-independent relation between the galaxy properties and the core images. Some real galaxies have diffuse cores that should yield bright core images (magnification μ_core 0.1), but more common are galaxies that yield faint core images (μ_core 0.001). Thus, stellar mass distributions alone are probably concentrated enough to explain the lack of observed core images. Observational sensitivity may need to improve by an order of magnitude before detections of core images become common. Two-image lenses should tend to have brighter core images than four-image lenses, so they will be the better targets for finding core images and exploiting these tools for studying the central mass distributions of distant galaxies.