When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for a system rotating at three times the current solar rotation rate. We find that substantial organized global-scale magnetic fields are achieved by dynamo action in this system. Striking wreaths of magnetism are built in the midst of the convection zone, coexisting with the turbulent convection. This is a surprise, for it has been widely believed that such magnetic structures should be disrupted by magnetic buoyancy or turbulent pumping. Thus, many solar dynamo theories have suggested that a tachocline of penetration and shear at the base of the convection zone is a crucial ingredient for organized dynamo action, whereas these simulations do not include such tachoclines. We examine how these persistent magnetic wreaths are maintained by dynamo processes and explore whether a classical mean-field $alpha$-effect explains the regeneration of poloidal field.