Blood clots must be stiff to stop hemorrhage yet elastic to buffer blood's shear forces. Upsetting this balance results in clot rupture and life-threatening thromboembolism. Fibrin, the main component of a blood clot, is formed from molecules of fibrinogen activated by thrombin. Although it is well known that fibrin possesses considerable elasticity, the molecular basis of this elasticity is unknown. Here, we use atomic force microscopy (AFM) and steered molecular dynamics (SMD) to probe the mechanical properties of single fibrinogen molecules and fibrin protofibrils, showing that the mechanical unfolding of their coiled-coil alpha helices is characterized by a distinctive intermediate force plateau in the systems' force-extension curve. We relate this plateau force to a stepwise unfolding of fibrinogen's coiled alpha helices and of its central domain. AFM data show that varying pH and calcium ion concentrations alters the mechanical resilience of fibrinogen. This study provides direct evidence for the coiled alpha helices of fibrinogen to bring about fibrin elasticity.