We present a measurement of the branching fraction for the rare decays B-->rhoenu and extract a value for the magnitude of V(ub), one of the smallest elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix. The results are given for five different calculations of form factors used to para-metrize the hadronic current in semileptonic decays. Using a sample of 55 x 10(6) BB meson pairs recorded with the BABAR detector at the PEP-II e(+)e(-) storage ring, we obtain B(B0-->rho(-)e(+)nu)=(3.29+/-0.42+/-0.47+/-0.55) x 10(-4) and |V(ub)|=(3.64+/-0.22+/-0.25(+0.39)(-0.56)) x 10(-3), where the uncertainties are statistical, systematic, and theoretical, respectively.