We have measured rapidity densities dN/dy of pi+/- and K+/- over a broad rapidity range (-0.1 < y < 3.5) for central Au + Au collisions at square root(sNN) = 200 GeV. These data have significant implications for the chemistry and dynamics of the dense system that is initially created in the collisions. The full phase-space yields are 1660 +/- 15 +/- 133 (pi+), 1683 +/- 16 +/- 135 (pi-), 286 +/- 5 +/- 23 (K+), and 242 +/- 4 +/- 19 (K-). The systematics of the strange to nonstrange meson ratios are found to track the variation of the baryochemical potential with rapidity and energy. Landau-Carruthers hydrodynamics is found to describe the bulk transport of the pions in the longitudinal direction.