We propose the realization of topological quantum states in a cold-atom system, using a two-dimensional hexagonal optical lattice and a light-induced periodic vector potential. A necessary condition for observing the topological states is the realization of a confining potential with a flat bottom and sharp boundaries. To probe the topological states, we propose to load bosons into the characteristic edge states and image them directly. The possibility of mapping out the edge states and controlling the optical lattice and vector potentials offers opportunities for exploring topological phases with no equivalent in condensed-matter systems.