  The butterfly velocity $v_B$ has been proposed as a characteristic velocity
for information propagation in local systems. It can be measured by the
ballistic spreading of local operators in time (or, equivalently, by
out-of-time-ordered commutators). In general, this velocity can depend on the
direction of spreading and, indeed, the asymmetry between different directions
can be made arbitrarily large using arbitrarily deep quantum circuits.
Nevertheless, in almost all examples of local time-independent Hamiltonians
that have been examined thus far, this velocity is independent of the direction
of information propagation. In this work, we present two models with asymmetric
$v_B$. The first is a time-independent Hamiltonian in one dimension with local,
3-site interactions. The second is a class of local unitary circuits, which we
call $n$-staircases, where $n$ serves as a tunable parameter interpolating from
$n=1$ with symmetric spreading to $n=\infty$ with completely chiral information
propagation.
