Second-order Moller–Plesset perturbation theory (MP2) is one of the simplest correlated wave-function methods, but its conventional O(N⁵) cost limits its application to large systems. Stochastic tensor contraction (STC) has recently appeared as a general technique to evaluate high-order tensor contractions in quantum chemistry. Here, we apply STC to the exchange contribution of Laplace-transformed MP2, which is the source of O(N⁵) scaling in the formulation. The resulting STC exchange algorithm has an O(N³) deterministic setup cost and an O(N²) stochastic cost at fixed absolute error. The estimator is unbiased and provides a way to specify the target stochastic error by estimating the number of required samples before the full calculation. We implement the algorithm using a hybrid deterministic–stochastic evaluation strategy, with grouped index sampling, to reduce the computational prefactor. Over a range of benchmark molecules containing up to ∼ 7000 basis functions, the stochastic exchange evaluation takes as little as 1/270 of the time of a complete DF-MP2 calculation on the same system. Within the Laplace-transformed formulation, the O(N⁴) scaling direct contribution is thus the only significant cost. Our results further substantiate the power of STC to serve as a general tensor-contraction engine for quantum chemistry.