  We present a three-dimensional Chern-Simons gravity based on a deformation of
the Maxwell algebra. This symmetry allows introduction of a non-vanishing
torsion to the Maxwell Chern-Simons theory, whose action recovers the
Mielke-Baelker model for particular values of the coupling constants. By
considering suitable boundary conditions, we show that the asymptotic symmetry
is given by the $\widehat{\mathfrak{bms}}_3\oplus\mathfrak{vir}$ algebra with
three independent central charges.
