The neutrino-induced nuclear transition l2 C(v e ,e ~) l2 N(g.s.) has been observed with a 15-ton finegrained tracking detector. The exclusive final state is identified by both an electron track and the positron decay of the ,2 N. From the observation of 181 ± 17 l2 C(v e ,e ~) ,2 N(g.s.) events with subsequent positron decays the flux-averaged cross section, equivalent to the cross section for 35.0-MeV neutrinos, is [1.05 ±0.10(stat) ±0.10(syst)] x 10 ~4 1 cm 2 . This result is in good agreement with recent calculations. PACS numbers: 25.30.Pt, 13.15.DkWe report the measurement of the cross section for l2 C(v e ,e ~) 12 N(g.s.) with v e from a beam-stop neutrino source. This is the first observation of an electron-neutrino-induced reaction between specific nuclear states. 1 Such exclusive reactions are of interest in nuclear physics, astrophysics, and particle physics. Recently, special attention has been drawn to the possibility of using exclusive neutrino reactions for solar-and supernovaneutrino detection. 2 Interpretation of the < t rate in any low-energy neutrino observatory require confidence in calculations for neutrino-induced nuclear transition rates. 3 Furthermore, it has been pointed out that certain specific neutrino-induced reactions may play a pivotal role in the production of intermediate-mass elements such as 19 F. 4 Yet, to date no experimental cross sections were available for neutrino-nucleus interactions to well-defined, two-body final states. This experiment observes such neutrino reactions at energies relevant for astrophysical observations and calculations. Our result provides useful checks of the theoretical calculations and serves as an experimental calibration.This reaction presents a simple case for theoretical calculations as the weak currents are known approximately from the corresponding 12 N p decay. Yet, the observed cross section is about 50% smaller than one estimates from just the 12 N(g.s.) decay rate, because the neutrino reaction occurs over a range of momentum transfers (q 2 ) for which nuclear form factors are important. It is possible to estimate these form factors using appropriate data (electron scattering, muon capture) in combination with the conserved-vector-current (CVC), weak-isospin, and other hypotheses. 5 Indeed, the l2 C(v e ,e ~) ,2 N(g.s.) transition rate is usually treated as