Silicon optomechanical crystals enable coupling of photons at telecommunication wavelengths to GHz mechanical modes, giving rise to optomechanical dynamics that can extend well into the resolved-sideband regime. Despite these promising characteristics, high-fidelity ground state preparation has to date only been achieved using passive cooling in a dilution refrigerator. Moreover, heating due to optical absorption has limited measurement protocols to short, low-energy optical pulses. Here, we demonstrate continuous-wave laser sideband cooling of a silicon optomechanical crystal to the zero-point energy, reaching a mean thermal occupancy of 0.09+0.02−0.01 quanta, or 92\% ground state occupation, self-calibrated via motional sideband asymmetry. Our results overcome previous limitations due to optical absorption heating and highlight optomechanical crystals for quantum-enhanced continuous displacement measurements, low-added-noise quantum transducers, and integration with superconducting qubit technology. *This work is supported by the Swiss National Science Foundation under grant No.~163387 and grant No.~51NF40-160591 (NCCR-QSIT), and the European Union’s Horizon 2020 research and innovation programme under grant No.~732894 (FET Proactive HOT).