We report on the first measurement of charm-strange meson D_{s}^{±} production at midrapidity in Au+Au collisions at sqrt[s_{NN}]=200 GeV from the STAR experiment. The yield ratio between strange (D_{s}^{±}) and nonstrange (D^{0}) open-charm mesons is presented and compared to model calculations. A significant enhancement, relative to a pythia simulation of p+p collisions, is observed in the D_{s}^{±}/D^{0} yield ratio in Au+Au collisions over a large range of collision centralities. Model calculations incorporating abundant strange-quark production in the quark-gluon plasma and coalescence hadronization qualitatively reproduce the data. The transverse-momentum integrated yield ratio of D_{s}^{±}/D^{0} at midrapidity is consistent with a prediction from a statistical hadronization model with the parameters constrained by the yields of light and strange hadrons measured at the same collision energy. These results suggest that the coalescence of charm quarks with strange quarks in the quark-gluon plasma plays an important role in D_{s}^{±}-meson production in heavy-ion collisions.