Langmuir films of a strongly chiral lipid, 1,2-bis(10,12 Tricosadiynoyl)-sn-Glycero-3-Phosphoethanolamine, form compact spiral and target patterns when compressed between two movable barriers in a Langmuir trough. These patterns are formed from 30C up to the gel transition at 38C. At lower temperatures, both left and right handed single-armed spirals form, with many defects, while at higher temperatures, the patterns form defect-free concentric circles. Critical pressures for pattern formation increase with increasing temperature. A possible mechanism is competition among elasticity, chirality, and the boundary conditions at the core of the domains.