We define a new compactification of outer space CVN (the \emph{Pacman
compactification}) which is an absolute retract, for which the boundary is a
Z-set. The classical compactification CVN made of very small
FN-actions on R-trees, however, fails to be locally 4-connected
as soon as N≥4. The Pacman compactification is a blow-up of
CVN, obtained by assigning an orientation to every arc with
nontrivial stabilizer in the trees.Comment: Final version. To appear in Annales de l'Institut Fourie