Silk is a natural fiber that surpasses most man-made polymers in its combination of strength and toughness. Silk fibroin, the primary protein component of silk, can be synthetically mimicked by a linear copolymer with alternating rigid and soft segments. Strategies for chemical synthesis of such silk-like polymers have persistently resulted in poor sequence control, long reaction times, and low molecular weights. Here, we present a two-stage approach for rapidly synthesizing silk-like polymers with precisely defined rigid blocks. This approach utilizes solid-phase peptide synthesis to create uniform oligoalanine "prepolymers", followed by microwave-assisted step-growth polymerization with bifunctional poly(ethylene glycol). Multiple coupling chemistries and reaction conditions were explored, with microwave-assisted click chemistry yielding polymers with M-w similar to 14 kg/mol in less than 20 min. These polymers formed antiparallel beta-sheets and nanofibers, which is consistent with the structure of natural silk fibroin. Thus, our strategy demonstrates a promising modular approach for synthesizing silk-like polymers.