We introduce the first comprehensive molecular model of spider dragline elasticity which clearly integrates most of the information known to date about the structure of the fiber. In accordance with X-ray evidence, the dragline is represented by a large number of small crystallites separated by amorphous regions made of rubber-like chains. Our model results clearly indicate the important role of the crystallites which act as multifunctional cross-links and create inside the amorphous regions a thin layer with modulus higher than in the bulk. The role of the crystallites in spider silk is found to be amazingly similar to that speculated for carbon black in synthesized elastomers.