  Let $(A,\mathfrak{m})$ be an analytically unramified Cohen-Macaulay local
ring of dimension $d \geq 3$ and let $\mathfrak{a}$ be an
$\mathfrak{m}$-primary ideal in $A$. If $I$ is an ideal in $A$ then let $I^*$
be the integral closure of $I$ in $A$. Let $G_{\mathfrak{a}}(A)^* =
\bigoplus_{n\geq 0 }(\mathfrak{a}^n)^*/(\mathfrak{a}^{n+1})^*$ be the
associated graded ring of the integral closure filtration of $\mathfrak{a}$.
Itoh conjectured in 1992 that if third Hilbert coefficient of
$G_{\mathfrak{a}}(A)^*$ , i.e., $e_3^{\mathfrak{a}^*}(A) = 0$ and $A$ is
Gorenstein then
  $G_{\mathfrak{a}}(A)^*$ is Cohen-Macaulay. In this paper we prove Itoh's
conjecture (more generally for analytically unramified Cohen-Macaulay local
rings).
