  We report the discovery of a faint H-alpha pulsar wind nebula (PWN) powered
by the radio pulsar B0740-28. The characteristic bow-shock morphology of the
PWN implies a direction of motion consistent with the previously measured
velocity vector for the pulsar. The PWN has a flux density more than an order
of magnitude lower than for the PWNe seen around other pulsars, but, for a
distance 2 kpc, it is consistent with propagation through a medium of atomic
density n_H ~ 0.25 cm^{-3}, and neutral fraction of 1%. The morphology of the
PWN in the area close to the pulsar is distinct from that in downstream
regions, as is also seen for the PWN powered by PSR B2224+65. In particular,
the PWN associated with PSR B0740-28 appears to close at its rear, suggesting
that the pulsar has recently passed through a transition from low density to
high density ambient gas. The faintness of this source underscores that deep
searches are needed to find further examples of optical pulsar nebulae.
