  We present WSRT observations of high sensitivity and resolution of the
neutral hydrogen in the starburst dwarf galaxy NGC 1569. Assuming a distance of
2.2 Mpc, we find a total HI mass of 1.3 * 10^8 M_sun to be distributed in the
form of a dense, clumpy ridge surrounded by more extended diffuse HI containing
a few additional discrete features, such as a Western HI Arm and an HI bridge
reaching out to a small counterrotating companion cloud. About 10% by mass of
all HI in NGC 1569 is at unusually high velocities. Some of this HI may be
associated with the mass outflow evident from H-alpha measurements, but some
may also be associated with NGC 1569's HI companion and intervening HI bridge,
in which case, infall rather than outflow might be the cause of the discrepant
velocities. No indication of a large bubble structure was found in
position-velocity maps of the high-velocity HI. The galaxy as a whole is in
modest overall rotation, but the HI gas lacks any sign of rotation within 60''
(0.6 kpc) from the center, i.e. over most of the optical galaxy. Here,
turbulent motions resulting from the starburst appear to dominate over
rotation. In the outer disk, the rotational velocities reach a maximum of 35
\pm 6 km/s, but turbulent motion remains significant. Thus, starburst effects
are still noticeable in the outer HI disk, although they are no longer dominant
beyond 0.6 kpc. Even excluding the most extreme high-velocity HI clouds, NGC
1569 still has an unusually high mean HI velocity dispersion of sigma_v=21.3
km/s, more than double that of other dwarf galaxies.
