  For an analytic and univalent function $f$ in the unit disk
$\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ with the normalization $f(0)=0=f'(0)-1$,
the logarithmic coefficients $\gamma_n$ are defined by $\log \frac{f(z)}{z}=
2\sum_{n=1}^{\infty} \gamma_n z^n$. In the present paper, we consider the class
of close-to-convex functions (with argument $0$), and determine the sharp upper
bound of $|\gamma_3|$ for such functions $f$, which proves a recent conjecture
of the first and third authors [1].
