An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $eta^{3/2}qlgg 1$, where $eta$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. Under this condition, the magnetoresistance scales as $eta^{7/2}$.
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