A sustainable triblock copolymer thermoplastic elastomer is developed containing a fatty acid‐derived midblock and salicylic acid‐derived endblocks. The rubbery midblock, poly(lauryl methacrylate), is chosen for its low glass transition temperature, hydrophobicity, and degradation resistance. Poly(acetylsalicylic ethyl methacrylate), derived from salicylic acid, abundantly encountered in plant products such as fruit and vegetable components, is developed as a biorenewable alternative for the glassy endblocks of the triblock copolymer. The acetylsalicylic ethyl methacrylate monomer offers advantages of the presence of carboxyl and hydroxyl groups, readily functionalized to acrylate or methacrylate groups, appropriate for controlled radical polymerization, and rigid aromatic rings which impart a high glass transition temperature to the polymer. The synthesis and characterization of poly(acetylsalicylic ethyl methacrylate‐block‐lauryl methacrylate‐block‐acetylsalicylic ethyl methacrylate) (ALA) triblock copolymers are presented. The ALA triblock copolymer exhibits microphase separated domains and is processable at elevated temperatures through compression molding. Tensile testing reveals elastomeric behavior at room temperature.