A high-security, high-speed stream cipher for physical-layer-secure optical communication, based on optical-carrier-induced private chaos synchronization and RC4 algorithm, is proposed and numerically demonstrated. The high security and speed are achieved by combining physical true random numbers generated from synchronized chaos, used as the key for random DNA coding, with the RC4 pseudo-random numbers. Moreover, no third-party signal is required as the optical carrier itself serves as the common drive for chaos synchronization in semiconductor lasers. To ensure privacy, phase encryption with confidential dispersion components is deployed at the communicating parties to encrypt the driving signals. A secure stream cipher exceeding 100 Gb/s, leveraging approximately 4 Gb/s physical random numbers to achieve a rate 32 times higher, has been numerically demonstrated. Additionally, it is also noted that pseudo-random numbers generated from different seeds can be encoded using the same physical true random numbers to create parallel stream ciphers, making this approach well-suited for wavelength-division-multiplexed and space-division-multiplexed high-speed optical communications.