As a by-product of high-precision, ultra-deep stellar photometry in the
Galactic globular cluster NGC 6397 with the Hubble Space Telescope, we are able
to measure a large population of background galaxies whose images are nearly
point-like. These provide an extragalactic reference frame of unprecedented
accuracy, relative to which we measure the most accurate absolute proper motion
ever determined for a globular cluster. We find mu_alpha = 3.56 +/- 0.04 mas/yr
and mu_delta = -17.34 +/- 0.04 mas/yr. We note that the formal statistical
errors quoted for the proper motion of NGC 6397 do not include possible
unavoidable sources of systematic errors, such as cluster rotation. These are
very unlikely to exceed a few percent. We use this new proper motion to
calculate NGC 6397's UVW space velocity and its orbit around the Milky Way, and
find that the cluster has made frequent passages through the Galactic disk.Comment: 5 pages including 3 figures, accepted for publication in the
Astrophysical Journal Letters. Very minor changes in V2. typos fixe
