The molecular tilt azimuth in domains of a condensed phase in monolayers of 1-monopalmytoyl-racglycerol at the air/water interface exhibits a regular star texture. Lateral-force microscopy has been used to investigate the friction behavior of a monolayer that has been transferred onto a silicon substrate. The condensed domains revealed strong friction anisotropies and asymmetries. The angular dependence of these properties correlates well with the tilt azimuth of the alkyl tails in the monolayer.