A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.