Using first-principles calculations, we report a large band-gap opening in the van der Waals heterostructure of graphene and graphane (hydrogenated graphene) under normal compressive (NC) strain. In the presence of graphane, interlayer charge transfer from graphene to graphane triggers the intralayer charge redistribution in graphene, breaking the equivalence of the two sublattices. This chiral symmetry breaking, however, is not strong enough to split the Dirac cone. The application of the NC strain enhances the inter-and intralayer charge transfer leading to a splitting of the Dirac cone, reflected as a redshift of the G peak in Raman spectra. With strain, the band gap increases monotonically and attains a maximum of 0.74 eV at 20% strain, which is the largest ever reported splitting of a Dirac cone in graphene. Tight-binding analysis demonstrates that the applied strain changes the on-site interactions of carbon atoms belonging to a particular sublattice of graphene, thereby breaking the chiral symmetry leading to the opening of a band gap. A sufficiently large band gap with linear dispersion of Dirac bands in the graphene/graphane heterostructure constitutes promising features for room-temperature electronic and optical devices.