  The U(1) gauge theory on a D3-brane with non-commutative worldvolume is shown
to admit BIon-like solutions which saturate a BPS bound on the energy. The
mapping of these solutions to ordinary fields is found exactly, namely
non-perturbatively in the non-commutativity parameters. The result is precisely
an ordinary supersymmetric BIon in the presence of a background B-field. We
argue that the result provides evidence in favour of the exact equivalence of
the non-commutative and the ordinary descriptions of D-branes.
