  We present the first observations of the Frontier Fields Cluster Abell S1063
taken with the newly commissioned Multi Unit Spectroscopic Explorer (MUSE)
integral field spectrograph. Because of the relatively large field of view (1
arcmin^2), MUSE is ideal to simultaneously target multiple galaxies in blank
and cluster fields over the full optical spectrum. We analysed the four hours
of data obtained in the Science Verification phase on this cluster and measured
redshifts for 53 galaxies. We confirm the redshift of five cluster galaxies,
and determine the redshift of 29 other cluster members. Behind the cluster, we
find 17 galaxies at higher redshift, including three previously unknown
Lyman-alpha emitters at z>3, and five multiply-lensed galaxies. We report the
detection of a new z=4.113 multiply lensed galaxy, with images that are
consistent with lensing model predictions derived for the Frontier Fields. We
detect C III], C IV, and He II emission in a multiply lensed galaxy at z=3.116,
suggesting the likely presence of an active galactic nucleus. We also created
narrow-band images from the MUSE datacube to automatically search for
additional line emitters corresponding to high-redshift candidates, but we
could not identify any significant detections other than those found by visual
inspection. With the new redshifts, it will become possible to obtain an
accurate mass reconstruction in the core of Abell S1063 through refined strong
lensing modelling. Overall, our results illustrate the breadth of scientific
topics that can be addressed with a single MUSE pointing. We conclude that MUSE
is a very efficient instrument to observe galaxy clusters, enabling their mass
modelling, and to perform a blind search for high-redshift galaxies.
