  We present the first NLO pQCD study of coherent exclusive $J/\psi$
photoproduction in ultraperipheral heavy-ion collisions (UPCs) at the LHC.
Taking the generalized parton distributions (GPDs) in their forward limit, as
parton distribution functions (PDFs), we quantify the NLO contributions in the
rapidity-differential cross section, show that the real part of the amplitude
must not be neglected, study the gluon and quark contributions, chart the
scale-choice and PDF uncertainties, and compare the NLO results with LHC and
HERA data. We show that the scale dependence is significant but a scale choice
can be found with which we reproduce the 2.76 and 5.02 TeV UPC data. In
particular, we show that the process is clearly more sensitive to the nuclear
quark PDFs than thought before.
