Poly-β-myrcene, a polyunsaturated hydrocarbon-type biopolymer contained in natural Chios mastic, a resin secreted by Chios mastic trees (Pistacia lentiscus L.) when wounded, is isolated from this gum and epoxidized with peracetic acid formed in-situ. The reaction product (epoxidized poly-beta-myrcene) is a sustainable self-curing epoxy polymer capable of serving as an adhesive or matrix for green composites. The parameters affecting the rate of this acid-catalyzed reaction (temperature, time, stirring rate, hydrogen peroxide concentration, acetic acid concentration, and catalyst type and concentration) are studied and the most favorable conditions are determined. Kinetic studies are then carried out to calculate reaction rate constants of the order of 10–6 L mol−1 s−1, for temperatures in the range of 35–55 °C, and activation energy of 59.22 kJ/mol. The thermodynamic parameters of activation enthalpy, entropy, and free energy, at 25 °C, were found equal to 13.56 kcal/mol, −41.10 cal/(mol K), and 12.22 kcal/mol, respectively. These findings lead to the optimization of reaction parameters and the kinetic/thermodynamic study of the promising poly-β-myrcene epoxide production process.