  We introduce a certain compactification of the space of projective
configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples
of points in $P^{k-1}$ in general position. This compactification differs
considerably from Mumford's geometric invariant theory quotient. It is obtained
by considering limit position (in the Chow variety) of the closures of generic
orbits. The same result will be obtained if we study orbits of the maximal
torus on the Grassmannian $G(k,n)$. We study in detail the closures of the
torus orbits and their "visible contours" which are Veronese varieties in the
Grassmannian. For points on $P^1$ our construction gives the Grothemdieck -
Knudsen moduli space of stable $n$ -punctured curves of genus 0. The "Chow
quotient" interpretation of this space permits us to represent it as a blow up
of a projective space.
