  Parity-violating physics in the early Universe can leave detectable traces in
late-time observables. Whilst vector- and tensor-type parity-violation can be
observed in the $B$-modes of the cosmic microwave background, scalar-type
signatures are visible only in the four-point correlation function (4PCF) and
beyond. This work presents a blind test for parity-violation in the 4PCF of the
BOSS CMASS sample, considering galaxy separations in the range
$[20,160]h^{-1}\mathrm{Mpc}$. The parity-odd 4PCF contains no contributions
from standard $\Lambda$CDM physics and can be efficiently measured using
recently developed estimators. Data are analyzed using both a non-parametric
rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a
compressed $\chi^2$ analysis, with the former avoiding the assumption of a
Gaussian likelihood. These find similar results, with the rank test giving a
detection probability of $99.6\%$ ($2.9\sigma$). This provides significant
evidence for parity-violation, either from cosmological sources or systematics.
We perform a number of systematic tests: although these do not reveal any
observational artefacts, we cannot exclude the possibility that our detection
is caused by the simulations not faithfully representing the statistical
properties of the BOSS data. Our measurements can be used to constrain physical
models of parity-violation. As an example, we consider a coupling between the
inflaton and a $U(1)$ gauge field and place bounds on the latter's energy
density, which are several orders of magnitude stronger than those previously
reported. Upcoming probes such as DESI and Euclid will reveal whether our
detection of parity-violation is due to new physics, and strengthen the bounds
on a variety of models.
