  It is possible to couple Dirac-Born-Infeld (DBI) scalars possessing
generalized Galilean internal shift symmetries (Galileons) to nonlinear massive
gravity in four dimensions, in such a manner that the interactions maintain the
Galilean symmetry. Such a construction is of interest because it is not
possible to couple such fields to massless General Relativity in the same way.
We show that this theory has the primary constraint necessary to eliminate the
Boulware-Deser ghost, thus preserving the attractive properties of both the
Galileons and ghost-free massive gravity.
