Time reversal invariance violation plays only a small role in the Standard Model, and the existence of a T-violating effect above the predicted level would be an indication of new physics. A sensitive probe of this symmetry in the weak interaction is the measurement of the T-violating ''D''-correlation in the decay of free neutrons. The triple-correlation D{sigma}{sub n}{center_dot}p{sub e} x p{sub v} involves three kinematic variables, the neutron spin, electron momentu, and neutrino (or proton) momentum, and changes sign under time reversal. This experiment detects the decay products of a polarized cold neutron beam with an octagonal array of scintillation and solid-state detectors. Data from first run at NIST's Cold Neutron Research Facility give a D-coefficient of -0.1 {+-} 1.3(stat.) {+-} 0.7(syst) x 10{sup -3}. This measurement has the greatest bearing on extensions to the Standard model that incorporate leptoquarks, although exotic fermion and lift-right symmetric models also allow a D as large as the present limit.