  Abridged - Stars with ZAMS masses between 140 and $260 M_\odot$ are thought
to explode as pair-instability supernovae (PISNe). During their thermonuclear
runaway, PISNe can produce up to several tens of solar masses of radioactive
nickel, resulting in luminous transients similar to some superluminous
supernovae (SLSNe). Yet, no unambiguous PISN has been discovered so far.
SN2018ibb is a H-poor SLSN at $z=0.166$ that evolves extremely slowly compared
to the hundreds of known SLSNe. Between mid 2018 and early 2022, we monitored
its photometric and spectroscopic evolution from the UV to the NIR with 2-10m
class telescopes. SN2018ibb radiated $>3\times10^{51} \rm erg$ during its
evolution, and its bolometric light curve reached $>2\times10^{44} \rm
erg\,s^{-1}$ at peak. The long-lasting rise of $>93$ rest-frame days implies a
long diffusion time, which requires a very high total ejected mass. The PISN
mechanism naturally provides both the energy source ($^{56}$Ni) and the long
diffusion time. Theoretical models of PISNe make clear predictions for their
photometric and spectroscopic properties. SN2018ibb complies with most tests on
the light curves, nebular spectra and host galaxy, potentially all tests with
the interpretation we propose. Both the light curve and the spectra require
25-44 $M_\odot$ of freshly nucleosynthesised $^{56}$Ni, pointing to the
explosion of a metal-poor star with a He-core mass of 120-130 $M_\odot$ at the
time of death. This interpretation is also supported by the tentative detection
of [Co II]$\lambda$1.025$\mu$m, which has never been observed in any other PISN
candidate or SLSN before. Powering by a central engine, such as a magnetar or a
black hole, can be excluded with high confidence. This makes SN2018ibb by far
the best candidate for being a PISN, to date.
