  We analytically prove that the existence of the delta-function singularity in
the chirally-odd twist-3 distribution $e(x)$ of the nucleon is inseparably
connected with the nonvanishing quark condensate as a signal of the spontaneous
chiral symmetry breaking of the QCD vacuum. This singularity in $e(x)$, which
would be observed as a sizable violation of the 1st moment sum rule, is then
interpreted as giving a very rare case that the nontrivial vacuum structure of
QCD manifests in an observable of a localized QCD excitation, i.e. the nucleon.
