The shapes of domain boundaries in the mesoscopic phase separation of phospholipids in aqueous surface monolayers are analyzed with particular attention to the influence of molecular chirality. We have calculated equilibrium shapes of such boundaries, and show that the concept of spontaneous curvature-derived from an effective pair potential between the chiral molecules-yields an adequate description of the contribution of chirality to the total energy of the system. For enantiomeric dipalmitoylphosphatidylcholine in pure monolayers, and in mixtures with impurities that adsorb preferentially at the (one-dimensional) boundary line between the isotropic and anisotropic fluid phases, such as cyanobiphenyl (5CB), a total energy term that includes line tension, electrostatic dipole-dipole interaction, and spontaneous curvature is sufficient to describe the shapes of well-separated domain boundaries in full detail. As soon as interdomain distances fall below the domain sizes upon compression of a monolayer, fluctuations take over in determining its detailed structural morphology. Using Minkowski measures for the well-studied dimyristoyl phosphatidic acid (DMPA)/cholesterol system, we show that calculations accounting for line tension, electrostatic repulsion, and molecular chirality yield boundary shapes that are of the same topology as the experimentally observed structures. At a fixed molecular area in the phase coexistence region, the DMPA/cholesterol system undergoes an exponential decay of the line tension lambda with decreasing subphase temperature T.