In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff–Schwartz algorithm: we basically replace the standard least squares regression with a Wiener chaos expansion. This not only allows us to deal with a non-Markovian setting but also breaks the bottleneck induced by the least squares regression, as the coefficients of the chaos expansion are given by scalar products on the L²(Ω) space and can therefore be approximated by independent Monte Carlo computations. This key feature enables us to propose an embarrassingly parallel algorithm to efficiently handle non-Markovian payoff.