  Let $X$ be a nonsingular variety defined over an algebraically closed field
of characteristic $0$, and $D$ be a free divisor with Jacobian ideal of linear
type. We compute the Chern class of the sheaf of logarithmic derivations along
$D$ and compare it with the Chern-Schwartz-MacPherson class of the hypersurface
complement. Our result establishes a conjecture by Aluffi raised in
\cite{hyparr}.
