This study investigates H(infinity) finite-time synchronization (HFTS) problems for a general class of chaotic systems with external disturbances. The HFTS includes two control objectives; one is the finite-time synchronization and the other is the H(infinity) minimization. Here, the finite-time synchronization means the finite-time stabilization of the error system between the master and slave chaotic systems, and the H(infinity) minimization denotes that the rate between the error system's output and external disturbance is constrained and minimized. Takagi-Sugeno (T-S) fuzzy models are utilized to represent the master and slave chaotic systems. The synthesized controller called H(infinity) finite-time synchronizing controller (HFSC) is composed of three sub-controllers, namely, one linear feedback control and two fuzzy parallel distributed compensation (PDC) controls. Finally, the controller synthesis procedure is summarized and simulation results are provided to demonstrate the validity and effectiveness of the proposed controllers.