  Graphene is the first model system of two-dimensional topological insulator
(TI), also known as quantum spin Hall (QSH) insulator. The QSH effect in
graphene, however, has eluded direct experimental detection because of its
extremely small energy gap due to the weak spin-orbit coupling. Here we predict
by ab initio calculations a giant (three orders of magnitude) proximity induced
enhancement of the TI energy gap in the graphene layer that is sandwiched
between thin slabs of Sb2Te3 (or MoTe2). This gap (1.5 meV) is accessible by
existing experimental techniques, and it can be further enhanced by tuning the
interlayer distance via compression. We reveal by a tight-binding study that
the QSH state in graphene is driven by the Kane-Mele interaction in competition
with Kekul\'e deformation and symmetry breaking. The present work identifies a
new family of graphene-based TIs with an observable and controllable bulk
energy gap in the graphene layer, thus opening a new avenue for direct
verification and exploration of the long-sought QSH effect in graphene.
