  The proton matrix element of the isovector-scalar density,
$<p|\overline{u}u-\overline{d}d|p>/2M_p$, is calculated by evaluating the
nucleon current correlation function in an external isovector-scalar field
using the QCD sum-rule method. In addition to the usual chiral and gluon
condensates of the QCD vacuum, the response of the chiral condensates to the
external isovector field enters the calculation. The latter is determined by
two independent methods. One relates it to the difference between the up and
down quark chiral condensates and the other uses the chiral perturbation
theory. To first order in the quark mass difference $\delta m=m_d-m_u$, the
non-electromagnetic part of the neutron-proton mass difference is given by the
product $\delta m <p|\overline{u}u-\overline{d}d|p>/2M_p$; the resulting value
is in reasonable agreement with the experimental value.
