The charged-particle pseudorapidity density dN(ch)/d eta has been measured for Au+Au collisions at sqrt[s(NN)] = 130 GeV at RHIC, using the PHOBOS apparatus. The total number of charged particles produced for the 3% most-central Au+Au collisions for /eta/<or=5.4 is found to be 4200+/-470. The evolution of dN(ch)/d eta with centrality is discussed, and compared to model calculations and to data from proton-induced collisions. The data show an enhancement in charged-particle production at midrapidity, while in the fragmentation regions, the results are consistent with expectations from pp and pA scattering.