We present the first measurement of the pseudorapidity density of primary charged particles in Au+Au collisions at root square[s(NN)] = 200 GeV. For the 6% most central collisions, we obtain dN(ch)/d(eta)/(/eta/<1) = 650+/-35(syst). Compared to collisions at root square[s(NN)] = 130 GeV, the highest energy studied previously, an increase by a factor of 1.14+/-0.05 at 90% confidence level, is found. The energy dependence of the pseudorapidity density is discussed in comparison with data from proton-induced collisions and theoretical predictions.