We present charged-particle multiplicities as a function of pseudorapidity and collision centrality for the 197Au+197Au reaction at square root[s(NN)] = 200 GeV. For the 5% most central events we obtain dN(ch)/deta/(eta = 0) = 625+/-55 and N(ch)/(-4.7< or =eta < or =4.7) = 4630 +/- 370, i.e., 14% and 21% increases, respectively, relative to square root[s(NN)] = 130 GeV collisions. Charged-particle production per pair of participant nucleons is found to increase from peripheral to central collisions around midrapidity. These results constrain current models of particle production at the highest RHIC energy.