We report on a search for neutrinoless double-beta decay of Xe-136 with EXO-200. No signal is observed for an exposure of 32.5 kg yr, with a background of similar to 1.5 x 10(-3) kg(-1) yr(-1) keV(-1) in the +/- 1 sigma region of interest. This sets a lower limit on the half-life of the neutrinoless double-beta decay T-1/2(0 nu beta beta) (Xe-136) > 1.6 x 10(25) yr (90% C. L.), corresponding to effective Majorana masses of less than 140-380 meV, depending on the matrix element calculation.