Using large-scale molecular dynamics simulations, we have shown previously that the spreading dynamics of sessile drops on solid surfaces can be described in detail using the molecular-kinetic theory of dynamic wetting. Here we present our first steps in extending this approach to investigate the spreading dynamics of Langmuir-Blodgett monolayers. We make use of a monolayer model originally developed by Karaborni and Toxvaerd, but somewhat simplified to facilitate large-scale simulations. Our preliminary results are in good agreement with recent experimental observations and also support a molecular-kinetic interpretation in which the driving force for spreading is the lateral pressure in the monolayer. Away from equilibrium, initial spreading rates are constant and logarithmically dependent on pressure. However, near equilibrium, spreading is pseudo-diffusive and follows the square root of time. In both regimes the controlling factor is the equilibrium frequency of molecular displacements within the monolayer.