We report direct imaging by means of x-ray photoemission electron microscopy of the dynamics of magnetic vortices confined in micron-sized circular permalloy dots that are 30 nm thick. The vortex core positions oscillate on a 10 ns time scale in a self-induced magnetostatic potential well after the in-plane magnetic field is turned off. The measured oscillation frequencies as a function of the aspect ratio of the dots are in agreement with theoretical calculations presented for the same geometry.