We report on the first demonstration of single sideband (SSB) modulated time stretch system. In addition, we present an analytical model relating the system performance to the phase and amplitude mismatches in the SSB modulator. The results show that, fortuitously, the system is tolerant to such mismatches. In particular, using commercially available components,the dispersion induced power penalty can be kept below 2.5 dB over 4-20 GHz bandwidth for any stretch factor. The experiments demonstrate 120 Gsample/s real-time capture of a 20 GHz SSB-modulated microwave signal.