This paper presents the first test of whether stochastic growth theory (SGT) can explain the detailed characteristics of Langmuir-like waves in Earth's foreshock. A period with unusually constant solar wind magnetic field is analyzed. The observed distributions P(log E) of wave fields E for two intervals with relatively constant spacecraft location (DIFF) are shown to agree well with the fundamental prediction of SGT, that P(log E) is Gaussian in log E. This stochastic growth can be accounted for semi-quantitatively in terms of standard foreshock beam parameters and a model developed for interplanetary type III bursts. Averaged over the entire period with large variations in DIFF, the P(log E) distribution is a power-law with index ~-1; this is interpreted in terms of convolution of intrinsic, spatially varying P(log E) distributions with a probability function describing ISEE's residence time at a given DIFF. Wave data from this interval thus provide good observational evidence that SGT can sometimes explain the clumping, burstiness, persistence, and highly variable fields of the foreshock Langmuir-like waves.¿ 1997 American Geophysical Union