  We study incoherent DVCS on $^4$He in the $^4{\rm He}(e,e^{\prime}\gamma p)X$
reaction, which probes medium-modifications of the bound nucleon GPDs and
elastic form factors. Assuming that the bound nucleon GPDs are modified in
proportion to the corresponding bound nucleon elastic form factors, as
predicted in the Quark-Meson Coupling model, we develop an approach to
calculate various incoherent nuclear DVCS observables. As an example, we
compute the beam-spin DVCS asymmetry, and predict the $x_B$- and $t$-dependence
of the ratio of the bound to free proton asymmetries, $A_{\rm
LU}^{p^{\ast}}(\phi)/A_{\rm LU}^{p}(\phi)$. We find that the deviation of
$A_{\rm LU}^{p^{\ast}}(\phi)/A_{\rm LU}^{p}(\phi)$ from unity is as much as
$\sim$ 6%.
