  We present a high-precision mass model of the galaxy cluster
MACSJ0416.1-2403, based on a strong-gravitational-lensing analysis of the
recently acquired Hubble Space Telescope Frontier Fields (HFF) imaging data.
Taking advantage of the unprecedented depth provided by HST/ACS observations in
three passbands, we identify 51 new multiply imaged galaxies, quadrupling the
previous census and bringing the grand total to 68, comprising 194 individual
lensed images. Having selected a subset of the 57 most securely identified
multiply imaged galaxies, we use the Lenstool software package to constrain a
lens model comprised of two cluster-scale dark-matter halos and 98 galaxy-scale
halos. Our best-fit model predicts image positions with an $RMS$ error of
0.68'', which constitutes an improvement of almost a factor of two over
previous, pre-HFF models of this cluster. We find the total projected mass
inside a 200~kpc aperture to be $(1.60\pm0.01)\times 10^{14}\ M_\odot$, a
measurement that offers a three-fold improvement in precision, reaching the
percent level for the first time in any cluster. Finally, we quantify the
increase in precision of the derived gravitational magnification of
high-redshift galaxies and find an improvement by a factor of $\sim$2.5 in the
statistical uncertainty. Our findings impressively confirm that HFF imaging has
indeed opened the domain of high-precision mass measurements for massive
clusters of galaxies.
