We report on the development of an instrument for the measurement of the longitudinal beam profile in the Large Hadron Collider (LHC). The technique used, which has been successfully demonstrated at the Advanced Light Source, mixes the synchrotron radiation with the light from a mode-locked solid state laser oscillator in a non-linear crystal. The up-converted radiation is then detected with a photomultiplier and processed to extract, store and display the required information. A 40 MHz laser, phase-locked to the ring radio frequency system, with a 50 ps pulse length, would be suitable for measuring the dynamics of the core of each of the LHC 2808 bunches in a time span much shorter than the synchrotron period. The same instrument could also monitor the evolution of the bunch tails, the presence of untrapped particles and their diffusion into nominally empty RF buckets ("ghost bunches") as required by the CERN specifications.