  If the neutrinos are Majorana fermions, there are at least three new,
potentially observable CP-odd phases that parameterize CP-invariance violating
phenomena. We currently have no information regarding any of them and know that
two out of the three, the so-called Majorana phases, are very hard to access
experimentally. Here, we discuss the effect of Majorana phases on
charged-lepton electric dipole moments (EDM), and explicitly show that neutrino
Majorana phases induce EDMs even in the absence of other sources of
CP-invariance violation. We also argue that while the Majorana neutrino
contribution to EDMs is tiny, there is one generic ultraviolet completion to
the standard model plus massive Majorana neutrinos -- the standard model plus a
triplet Higgs boson -- that leads to significantly enhanced contributions which
are still proportional to the low-energy neutrino Majorana phases. If this
particular scenario is realized in nature, it seems possible, at least in
principle, to measure the Majorana phases by precisely measuring charged-lepton
EDMs.
