  Following up on a faint detection of a near-infrared (NIR) source at the
position of the X-ray thermal isolated neutron star RX J0806.4-4123, we present
new Hubble Space Telescope observations in the H-band. The NIR source is
unambiguously detected with a Vega magnitude of 23.7 +/- 0.2 (flux density of
0.40 +/- 0.06 microJy at lambda =1.54 microm. The source position is coincident
with the neutron star position, and the implied NIR flux is strongly in excess
of what one would expect from an extrapolation of the optical-UV spectrum of RX
J0806.4-4123. The NIR source is extended with a size of at least 0.8arcsec and
shows some asymmetry. The conservative upper limit on the flux contribution of
a point source is 50%. Emission from gas and dust in the ambient diffuse
interstellar medium can be excluded as cause for the extended emission. The
source parameters are consistent with an interpretation as either the first
NIR-only detected pulsar wind nebula or the first resolved disk around an
isolated neutron star.
