  Lepton flavor violating Higgs decays can arise in flavor symmetry models
where the Higgs sector is responsible for both the electroweak and the flavor
symmetry breaking. Here we advocate an $S_4$ three-Higgs-doublet model where
tightly constrained flavor changing neutral currents are suppressed by a
remnant $Z_3$ symmetry. A small breaking of this $Z_3$ symmetry can explain the
$2.4\,\sigma$ excess of Higgs decay final states with a $\mu \tau $ topology
reported recently by CMS if the new neutral scalars are light. The model also
predicts sizable rates for lepton flavor violating Higgs decays in the $e\tau $
and $e \mu$ channels because of the unifying $S_4$ flavor symmetry.
