Complexes of fully ionized third-generation dendrimers with oppositely charged linear polyelectrolyte chains are studied by the Brownian dynamics method. A freely jointed model of a dendrimer and a linear chain is used. Electrostatic interactions are considered within the Debye-Hückel approximation with the Debye radius exceeding the dimensions of a dendrimer. In these systems, the phenomenon of charge inversion is observed, and the degree of "overcharging" is higher as compared with that taking place in analogous complexes formed by dendrimers in which only terminal groups are charged. The dependence of the amount of chain units adsorbed on a dendrimer on the polyelectrolyte chain length is nonmonotnic and agrees qualitatively with the predictions of the theory proposed by Nguyen and Shklovskii for a complex composed of a spherical macroion with an oppositely charged linear chain. This nonmonotonic character also manifests itself for certain other structural characteristics of the complexes. Upon the formation of a complex, a chain is shown to penetrate deeply into a dendrimer.