  We propose a new scenario of neutrino masses with a Higgs triplet
$(\xi^{++},\xi^+,\xi^0)$ in a theory of large extra dimensions. Lepton number
violation in a distant brane acts as the source of a very small trilinear
coupling of $\xi$ to the standard Higgs doublet in our brane. Small realistic
Majorana neutrino masses are \underline{naturally} obtained with the
fundamental scale $M_* \sim {\cal O}(1)$ TeV, foretelling the possible
discovery of $\xi$ $(m_\xi\lsim M_*)$ at future colliders. Decays of $\xi^{++}$
into same-sign dileptons are fixed by the neutrino mass matrix. Observation of
$\mu-e$ conversion in nuclei is predicted.
