  We propose and study the inclusive production of a forward $J/\psi$ and a
very backward jet at the LHC as an observable to reveal high-energy resummation
effects \`a la BFKL. Our different predictions are based on the various
existing mechanisms to describe the production of the $J/\psi$, namely, NRQCD
singlet and octet contributions, and the color evaporation model.
