  General relativistic effects have long been predicted to subtly influence the
observed large-scale structure of the universe. The current generation of
galaxy redshift surveys have reached a size where detection of such effects is
becoming feasible. In this paper, we report the first detection of the redshift
asymmetry from the cross-correlation function of two galaxy populations which
is consistent with relativistic effects. The dataset is taken from the Sloan
Digital Sky Survey DR12 CMASS galaxy sample, and we detect the asymmetry at the
$2.7\sigma$ level by applying a shell-averaged estimator to the
cross-correlation function. Our measurement dominates at scales around $10$
h$^{-1}$Mpc, larger than those over which the gravitational redshift profile
has been recently measured in galaxy clusters, but smaller than scales for
which linear perturbation theory is likely to be accurate. The detection
significance varies by 0.5$\sigma$ with the details of our measurement and
tests for systematic effects. We have also devised two null tests to check for
various survey systematics and show that both results are consistent with the
null hypothesis. We measure the dipole moment of the cross-correlation
function, and from this the asymmetry is also detected, at the $2.8 \sigma$
level. The amplitude and scale-dependence of the clustering asymmetries are
approximately consistent with the expectations of General Relativity and a
biased galaxy population, within large uncertainties. We explore theoretical
predictions using numerical simulations in a companion paper.
