The effect of the chirality on the thermodynamic behavior, the morphological features, and the 2D crystal structures of I-stearylamine-glycerol monolayers are studied. The results are based on measurements of the surface pressure-area (pi-A) isotherms, fluorescence microscopy, and synchrotron X-ray diffraction at grazing incidence (GIXD). Although the pi-A isotherms of the enantiomeric forms and the racemic mixtures agree largely to each other, the filigree domain patterns show remarkable differences, obviously driven by the chirality. The domains of the R(+) enantiomer are curved clockwise, those of the S(-) enantiomer counterclockwise, whereas those of the racemic mixtures are without a specific sense of direction. Chiral discrimination effects are also found in the lattice structure. The enantiomeric monolayers have an oblique lattice where at compression the tilt direction changes continuously from angles nearly toward NN direction to angles nearly toward NNN direction. The condensed phases of the 1:1 racemic mixtures give rise to rectangular-centered lattices indicating a phase transition accompanied by the change in the tilt direction from NN at 1 mN/m to NNN at 5 mN/m. The filigree domain patterns indicate a comparatively low ordering of the alkyl chains. Correspondingly, a short-range translational order can be concluded from the low position correlation and high tilt angles of the alkyl chains at low surface pressures.