  In this note we study the higher dimensional convex billiards satisfying the
so-called Gutkin property. A convex hypersurface $S$ satisfies this property if
any chord $[p,q]$ which forms angle $\delta$ with the tangent hyperplane at $p$
has the same angle $\delta$ with the tangent hyperplane at $q$. Our main result
is that the only convex hypersurface with this property in $\mathbf{R}^d, d\geq
3$ is a round sphere. This extends previous results on Gutkin billiards
obtained in \cite{B0}.
