Much experimental effort to realize possible uses of dendrimers has focused on the complexation of charged dendrimers to oppositely charged polyelectrolytes to form controlled delivery systems. Employing computer simulation and theory, we present a molecular-level picture bf these guest-host aggregates and the conditions necessary for forming them. Specifically, we examine the equilibrium and dynamic complexation behavior of a monocentric dendrimer with charged terminal groups to a flexible, oppositely charged polyelectrolyte. Three different types of complexes are noted depending upon the solution ionic strength and the sizes of the dendrimer and chain. We find that a dendrimer may encapsulate a chain, a chain and a dendrimer may mutually interpenetrate, or a unique "chain-walking" phenomenon may be observed. The critical conditions for complexation, density profiles of the polyelectrolyte and the dendrimer In the complex, and the curious dynamics observed are discussed. A closed formula is proposed to describe the critical conditions for complexation between a dendrimer and a polyelectrolyte.