Small neutrino masses and their large mixing angles can be generated at the
TeV scale by augmenting the Standard Model with an additional generation
dependent, anomaly-free U(1)_{nu} symmetry, in the presence of three
right-handed neutrinos. The Z' gauge boson associated with the breaking of the
U(1)_{nu} symmetry can be produced at the LHC. The flavorful nature of the Z'
can be established by measuring its non-universal couplings to the charged
leptons as determined by the lepton's U(1)_{nu} charges, which also govern the
neutrino flavor structure. While the LHC has the potential of discovering the
Z' up to M_{Z'} = 4.5 TeV with 100 fb^(-1) data at the center of mass energy
sqrt{s} = 14 TeV, to establish the flavorful nature of the Z' requires much
higher integrated luminosity. For our bench mark parameters that are consistent
with neutrino oscillation data, at sqrt{s} = 14 TeV, a 5 sigma distinction
between the dielectron and dimuon channels for M_{Z'} = 3 TeV requires 500
fb^(-1) of data. We find that the forward backward asymmetry distributions can
also be useful in distinguishing the dielectron and dimuon channels in the low
invariant mass and transverse momentum regions.Comment: 9 pages, 13 figures; v2: version to appear in Phys. Rev.