  We present a numerical study of exciton-polariton (polariton) condensation in
a staggered polariton graphene showing a gapped s-band at the $K$ and $K'$
valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorable
negative mass extrema of the valence band. Considering attractive
polariton-polariton interaction allows to generate a spatially extended
condensate. Spontaneous symmetry breaking occurring during the condensate
build-up leads to the formation of valley-polarized domains following the
Kibble-Zurek scenario. The selection of a single valley breaks time-reversal
symmetry and the walls separating domains exhibit a topologically-protected
chiral current. This current therefore emerges as a result of the interplay
between the non-trivial valley topology and the condensation-induced symmetry
breaking.
