  We consider Kapranov's Chow quotient compactification of the moduli space of
ordered n-tuples of hyperplanes in P^{r-1} in linear general position. For r=2
this is canonically identified with the Grothendieck-Knudsen compactification
of M_{0,n} which has among others the nice properties 1) Modular meaning:
stable pointed rational curves 2) Canonical description of limits of one
parameter degenerations 3) Natural Mori theoretic meaning: log canonical
compactification. We prove (1-2) generalize naturally to all (r,n), but that
(3), which we view as the deepest, fails except possibly in the cases
(2,n),(3,6),(3,7),(3,8), where we conjecture it holds. The same generalization
of (1) was given recently (and independently) by Hacking.
