The classical molecular dynamics simulations presented here examine the tribology associated with the sliding of a hydrogen-terminated diamond counterface across a monolayer of n-alkane chains that are covalently bound to a diamond substrate. Two systems using chains of fixed length (18 carbon atoms per chain) on diamond (111) are examined: a tightly packed (2 x 2) arrangement and a loosely packed system with approximately 30% fewer chains. Both systems give a similar average friction at low loads. Under high loads, the tightly packed monolayer exhibits significantly lower friction than the loosely packed monolayer. While the movement of chains is greatly constricted in both systems, the tightly packed monolayer under high loads is clearly more uniform in geometry and more constrained with respect to the movement of individual chains than the loosely packed monolayer. This suggests that efficient packing of the chains is responsible for the lower friction for tight packing under high load. This is supported by the fact that sliding initiates larger bond-length fluctuations in the loosely packed system, which ultimately lead to more energy dissipation via vibration.