  We provide a new extension of general relativity (GR) which has the
remarkable property of being more constrained than GR plus a cosmological
constant, having one less free parameter. This is implemented by allowing the
cosmological constant to have a consistent space-time variation, through coding
its dynamics in the torsion tensor. We demonstrate this mechanism by adding a
`quasi-topological' term to the Einstein action, which naturally realizes a
dynamical torsion with an automatic satisfaction of the Bianchi identities.
Moreover, variation of the action with respect to this dynamical $\Lambda$
fixes it in terms of other variables, thus providing a scenario with less
freedom than general relativity with a cosmological constant. Once matter is
introduced, at least in the homogeneous and isotropic reduction, $\Lambda$ is
uniquely determined by the field content of the model. We make an explicit
construction using the Palatini formulation of GR and describe the striking
properties of this new theory. We also highlight some possible extensions to
the theory. A companion paper [1] explores the Friedmann--Robertson--Walker
reduction for cosmology, and future work will study Solar System tests of the
theory.
