The v=1-->0 radiative lifetime of NH(X(3)Sigma(-),v=1,N=0) is determined to be tau_(rad,exp.)=37.0+/-0.5_(stat)+2.0/-0.8_(syst) ms, corresponding to a transition dipole moment of |mu_(10)|=0.0540_(-0.0018)(+0.0009) D. To achieve sufficiently long observation times, NH(X;{3}Sigma;{-},v=1) radicals are magnetically trapped using helium buffer-gas loading. The rate constant for background helium-induced collisional quenching was determined to be k_(v=1)<3.9x10(-15) cm(3) s(-1), which yields the quoted systematic uncertainty on tau_{rad,exp.}. With a new ab initio dipole moment function and a Rydberg-Klein-Rees potential, we calculate a lifetime of 36.99 ms, in agreement with our experimental value.