  We demonstrate that radiative breaking of conformal symmetry (and
simultaneously electroweak symmetry) in the Standard Model with right-chiral
neutrinos and a minimally enlarged scalar sector induces spontaneous breaking
of lepton number symmetry, which naturally gives rise to an axion-like particle
with some unusual features. The couplings of this `axion' to Standard Model
particles, in particular photons and gluons, are entirely determined (and
computable) via the conformal anomaly, and their smallness turns out to be
directly related to the smallness of the masses of light neutrinos.
