  This work proposes a new gravitational theory formulated in terms of the
vierbein field. The vierbein contains components which can be shifted by local
Lorentz transformations and therefore do not show up in the spacetime metric.
These components are given dynamics and become physical in our setup. They
enter the massless theory in the form of an antisymmetric tensor field which
makes the action reminiscent of the bosonic sector of supergravity. We then
demonstrate that both the metric and the antisymmetric tensor can be made
massive by adding a potential term for the vierbein. The form of this mass
potential is inspired by ghost-free massive gravity. We confirm the absence of
additional and potentially pathological degrees of freedom in an ADM analysis.
However, at the linearized level around maximally symmetric solutions, the
fluctuation of the antisymmetric tensor has a tachyonic mass pole.
