  HR8799 is orbited by at least four giant planets, making it a prime target
for the recently commissioned Spectro-Polarimetric High-contrast Exoplanet
REsearch (VLT/SPHERE). As such, it was observed on five consecutive nights
during the SPHERE science verification in December 2014. We aim to take full
advantage of the SPHERE capabilities to derive accurate astrometric
measurements based on H-band images acquired with the Infra-Red Dual-band
Imaging and Spectroscopy (IRDIS) subsystem, and to explore the ultimate
astrometric performance of SPHERE in this observing mode. We also aim to
present a detailed analysis of the orbital parameters for the four planets. We
report the astrometric positions for epoch 2014.93 with an accuracy down to 2.0
mas, mainly limited by the astrometric calibration of IRDIS. For each planet,
we derive the posterior probability density functions for the six Keplerian
elements and identify sets of highly probable orbits. For planet d, there is
clear evidence for nonzero eccentricity ($e \simeq 0.35$), without completely
excluding solutions with smaller eccentricities. The three other planets are
consistent with circular orbits, although their probability distributions
spread beyond $e = 0.2$, and show a peak at $e \simeq 0.1$ for planet e. The
four planets have consistent inclinations of about $30\deg$ with respect to the
sky plane, but the confidence intervals for the longitude of ascending node are
disjoint for planets b and c, and we find tentative evidence for
non-coplanarity between planets b and c at the $2 \sigma$ level.
