  The Shi arrangement due to Shi (1986) and the Ish arrangement due to
Armstrong (2013) are deformations of the type $A$ Coxeter arrangement that
share many common properties. Motivated by a question of Armstrong and Rhoades
since 2012 to seek for Ish arrangements of other types, in this paper we
introduce an Ish arrangement of type $B$. We study this Ish arrangement through
various aspects similar to as known in type $A$ with a main emphasis on
freeness and supersolvability. Our method is based on the concept of
$\psi$-digraphic arrangements recently introduced due to Abe and the authors
with a type $B$ extension.
