  Let $X^v_w$ be a Richardson variety in the full flag variety $X$ associated
to a symmetrizable Kac-Moody group $G$. Recall that $X^v_w$ is the intersection
of the finite dimensional Schubert variety $X_w$ with the finite codimensional
opposite Schubert variety $X^v$. We give an explicit $\bQ$-divisor $\Delta$ on
$X^v_w$ and prove that the pair $(X^v_w, \Delta)$ has Kawamata log terminal
singularities. In fact, $-K_{X^v_w} - \Delta$ is ample, which additionally
proves that $(X^v_w, \Delta)$ is log Fano.
  We first give a proof of our result in the finite case (i.e., in the case
when $G$ is a finite dimensional semisimple group) by a careful analysis of an
explicit resolution of singularities of $X^v_w$ (similar to the BSDH resolution
of the Schubert varieties). In the general Kac-Moody case, in the absence of an
explicit resolution of $X^v_w$ as above, we give a proof that relies on the
Frobenius splitting methods. In particular, we use Mathieu's result asserting
that the Richardson varieties are Frobenius split, and combine it with a result
of N. Hara and K.-I. Watanabe relating Frobenius splittings with log canonical
singularities.
