<p>The existence of global martingale solutions to a stochastic degenerate cross-diffusion system is shown. Previous results have shown that for some non-degenerate stochastic cross-diffusion systems, martingale solutions exist. When the degeneration phenomenon is involved, the existence of a martingale solution analysis has largely been complicated. In this work, through an advanced tightness proof scheme, we derive that a martingale solution indeed exists to a most typical stochastic degenerate cross-diffusion system with the volume-filling effect.</p>