Heterodyne generation of parallel random bit streams from chaotic emission of an optically injected semiconductor laser is investigated. The continuous-wave optical injection invokes chaotic dynamics in the laser. The broadband chaotic emission is detected through optical heterodyning and electrical heterodyning into different channels. The channels digitize the signals into parallel independent random bit streams. Because of efficient utilization of different portions of the chaos bandwidth, heterodyne detections enable parallel generation of random bit streams, offer high total output bit rates, and require no high-bandwidth analogue-to-digital converters. In the experiment, two optical heterodyne channels and four electrical heterodyne channels are implemented. Each channel is required to digitize only 2.5 GHz of a much broader chaos bandwidth. The sampling rate is 10 GHz with five least significant bits selected from every 8-bit sample. The total output bit rate reaches 100 Gb/s and 200 Gb/s for optical and electrical heterodyning, respectively. The standard test suite of the National Institute of Standards and Technology verifies the randomness of both individual and interleaved output bit streams.