  Four-dimensional homogeneous static and rotating black strings in dynamical
Chern-Simons modified gravity, with and without torsion, are presented. Each
solution is supported by a scalar field that depends linearly on the coordinate
that span the string. The solutions are locally $\mbox{AdS}_3 \times
\mathbb{R}$ and they represent the continuation of the
Ba\~nados-Teitelboim-Zanelli black hole. Moreover, they belong to the so-called
Chern-Simons sector of the space of solutions of the theory, since the Cotton
tensor contributes nontrivially to the field equations. The case with
nonvanishing torsion is studied within the first-order formalism of gravity,
and it considers nonminimal couplings of the scalar fields to three topological
invariants: Nieh-Yan, Pontryagin and Gauss-Bonnet terms, which are studied
separately. These nonminimal couplings generate torsion in vacuum, in contrast
to Einstein-Cartan theory. In all cases, torsion contributes to an effective
cosmological constant that, in particular cases, can be set to zero by a proper
choice of the parameters.
