The real-space dynamics in a model system of colloidal hard spheres was studied by means of time-resolved fluorescence confocal scanning microscopy. Direct experimental evidence for the presence of dynamical heterogeneities in a dense liquid was obtained from an analysis of particle trajectories in two-dimensional slices of the bulk sample. These heterogeneities manifest themselves as a non-Gaussian probability distribution of particle displacements and also affect the onset of long-time diffusive behavior.