  This letter reports results from a search for muon-neutrino to
electron-neutrino transitions by the MINOS experiment based on a 7x10^20
protons-on-target exposure. Our observation of 54 candidate electron-neutrino
events in the Far Detector with a background of 49.1+/-7.0(stat.)+/-2.7(syst.)
events predicted by the measurements in the Near Detector requires
2sin^2(2theta_{13})sin^2(theta_{23})<0.12 (0.20) at the 90% C.L. for the normal
(inverted) mass hierarchy at delta_cp=0. The experiment sets the tightest
limits to date on the value of theta_{13} for nearly all values of delta_cp for
the normal neutrino mass hierarchy and maximal sin^2(2theta_{23}).
