  We investigate within a quark-meson coupling (QMC) model, the structure of
the bound $\Xi^-$ hypernucleus $^{15}{\!\!\!_{\Xi^-}}$C ($^{14}$N + $\Xi^-$),
which has been observed in a recent analysis of the KEK-E373 experiment. In the
QMC model, light quarks in nonoverlapping nucleon and $\Xi^-$ bags interact
self-consistently with isoscalar-scalar ($\sigma$), isoscalar-vector
($\omega$), and isovector-vector ($\rho$) mesons in the mean field
approximation. The parameters of the model (quark-meson coupling constants and
masses) are mostly fixed from the nuclear matter saturation properties. The QMC
model closely reproduces the separation energies of the two $\Xi^-$ hyperon
states in $^{15}{\!\!\!_{\Xi^-}}$C reported in the KEK-E373 analysis, and
identifies their quantum numbers. We also make predictions for the cross
sections for the production of the $^{15}{\!\!\!_{\Xi^-}}$C hypernuclear specta
in the ($K^-, K^+$) reaction on a $^{15}$O target within a covariant effective
Lagrangian model using the $\Xi^-$ bound state spinors obtained within the same
QMC model.
