The space of ordered n-tuples of points on a projective line has a compactification, due to Grothendieck and Knudsen, with many remarkable properties: it has a natural moduli interpretation, namely it is the moduli space of stable n-pointed rational curves. It has a natural Mori theoretic meaning, namely it is the log canonical model of the interior. For a curve in the interior, there is a description of the limiting stable n-pointed rational curve, due to Kapranov, in terms of the Tits tree of $PGL_2$. We study these properties for the higher-dimensional versions of the Grothendieck-Knudsen space, the Chow quotients of Grassmannians.