  A line arrangement of $3n$ lines in $\mathbb CP^2$ satisfies Hirzebruch
property if each line intersect others in $n+1$ points. Hirzebruch asked if all
such arrangements are related to finite complex reflection groups. We give a
positive answer to this question in the case when the line arrangement in
$\mathbb CP^2$ is real, confirming that there exist exactly four such
arrangements.
