The ratios of charged antiparticles to particles have been obtained for pions, kaons, and protons near midrapidity in central Au+Au collisions at sqrt[sNN]=200 GeV. Ratios of 〈π-〉/〈π+〉=1.025±0.006(stat.)±0.018(syst.), 〈K-〉/〈K+〉=0.95±0.03(stat.)±0.03(syst.), and 〈p̅ 〉/〈p〉=0.73±0.02(stat.)±0.03(syst.) have been observed. The 〈K-〉/〈K+〉 and 〈p̅ 〉/〈p〉 ratios are consistent with a baryochemical potential μB of 27 MeV, roughly a factor of 2 smaller than in sqrt[sNN]=130 GeV collisions. The data are compared to results from lower energies and model calculations. Our accurate measurements of the particle ratios impose stringent constraints on current and future models dealing with baryon production and transport.