We demonstrate a single-chip silicon optical single sideband (OSSB) modulator composed of a radio frequency (RF) branch line coupler (BLC) and a silicon dual-parallel Mach–Zehnder modulator (DP-MZM). A co-design between the BLC and the DP-MZM is implemented to improve the sideband suppression ratio (SSR). The modulator has a modulation efficiency of $V_{\pi }{L}_{\pi }\sim 1.75\mathrm{V}·\mathrm{cm}$ and a 3 dB electro-optical (EO) bandwidth of 48.7 GHz. The BLC can generate a pair of RF signals with equal amplitudes and orthogonal phases at the optimal frequency of 21 GHz. We prove through theoretical calculation and experiment that, although the BLC’s performance in terms of power balance and phase orthogonality deteriorates in a wider frequency range, high SSRs can be realized by adjusting relevant bias phases of the DP-MZM. With this technique, the undesired sidebands are completely suppressed below the noise floor in the frequency range from 15 GHz to 30 GHz when the chip operates in the full carrier OSSB (FC-OSSB) mode. In addition, an SSR $>35\mathrm{dB}$ and an carrier suppression ratio (CSR) $>42\mathrm{dB}$ are demonstrated at 21 GHz in the suppressed carrier OSSB (SC-OSSB) mode.