We explicitly construct massive (0,4) supersymmetric ADHM sigma models
which have heterotic p-brane solitons as their conformal fixed points
. These yield the familiar gauge 5-brane and a new 1-brane solution wh
ich preserve half and a quarter of the space-time supersymmetry, respe
ctively. We also discuss an analogous construction for the type II NS-
NS p-branes using (4,4) supersymmetric models.