A new method is described for the Monte Carlo evaluation of integrals of the form exp [iS (x)]
that occur in the Feynman path integral representation of the time evolution operator, exp (−
iHt/h). The method is general, strictly Monte Carlo based (and thus applicable to high
dimensionality), and has the desirable feature that the stationary phase (ie semiclassical)
approximation to the integral is obtained in its worst limit. Application to a non-trivial test
case (the Airy integral) illustrates these features.