  We present the generalisation to (3+1) dimensions of a quantum deformation of
the (2+1) (Anti)-de Sitter and Poincar\'e Lie algebras that is compatible with
the conditions imposed by the Chern-Simons formulation of (2+1) gravity. Since
such compatibility is automatically fulfilled by deformations coming from
Drinfel'd double structures, we believe said structures are worth being
analysed also in the (3+1) scenario as a possible guiding principle towards the
description of (3+1) gravity. To this aim, a canonical classical $r$-matrix
arising from a Drinfel'd double structure for the three (3+1) Lorentzian
algebras is obtained. This $r$-matrix turns out to be a twisted version of the
one corresponding to the (3+1) $\kappa$-deformation, and the main properties of
its associated noncommutative spacetime are analysed. In particular, it is
shown that this new quantum spacetime is not isomorphic to the
$\kappa$-Minkowski one, and that the isotropy of the quantum space coordinates
can be preserved through a suitable change of basis of the quantum algebra
generators. Throughout the paper the cosmological constant appears as an
explicit parameter, thus allowing the (flat) Poincar\'e limit to be
straightforwardly obtained.
