Refractory high-entropy alloys (RHEAs) are a promising class of materials with potential applications in extreme environments, where the dominant failure mode is thermal creep. The design of these alloys, therefore, requires an understanding of how their microstructure and local chemical distribution affect creep behavior. In this study, we performed high-fidelity atomistic simulations using machine-learning interatomic potentials to explore the creep deformation of MoNbTaW RHEAs under a wide range of stress and temperature conditions. We parametrized grain size and local chemical order (LCO) to investigate the effects of these two important design variables, which are controllable during the alloy fabrication process. Our investigation revealed that resistance to creep deformation is enhanced by larger grain sizes and higher levels of LCO. This study highlights the importance of utilizing LCO in conjunction with other microstructural properties when designing RHEAs for extreme environment applications.