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.