  Borcea-Voisin threefolds provided some of the first examples of mirror pairs
in the Hodge-theoretic sense, but their mirror symmetry at the quantum level
have not previously been shown. We prove a Givental-style quantum mirror
theorem for certain Borcea-Voisin threefolds: by means of certain birational
models, we show that their Gromov-Witten J-functions are related by a mirror
map to solutions of the multi-parameter Picard-Fuchs equations coming from the
variation of Hodge structures of their mirror partners.
