Autoxidation of tartaric acid in air-saturated aqueous solutions in the presence of Fe(II) at low pH, 2.5, shows autocatalytic behavior with distinct initiation, propagation, and termination phases. With increasing pH, the initiation phase speeds up, while the propagation phase shortens and reduces to none. We show that the propagation phase is a chain reaction that occurs via activation of oxygen in the initiation stage with the production of hydrogen peroxide. The subsequent Fenton oxidation that regenerates hydrogen peroxide with a positive feedback is typical of a self-sustained chain reaction. The conditions for such a chain reaction are shown to be similar to those of a dynamical system with critical behavior; namely, the system becomes unstable when the kinetic matrix of pseudo-first-order reaction becomes negatively defined with a negative eigenvalue giving the rate of exponential (chain) growth of the reactive species.