  We consider the Cohen-Macaulay compactification of the space of twisted
cubics in projective n-space. This compactification is the fine moduli scheme
representing the functor of CM-curves with Hilbert polynomial 3t+1. We show
that the moduli scheme of CM-curves in projective 3-space is isomorphic to the
twisted cubic component of the Hilbert scheme. We also describe the
compactification for twisted cubics in n-space.
