We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\} into the Langevin algorithm and the observables and to perform the expansion in \beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by one loop the previously known series.
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