Probabilistic k-testable models (usually known as k-gram models in the case of strings) can be easily identified from samples and allow for smoothing techniques to deal with unseen events during pattern classification. In this paper, we introduce the family of stochastic k-testable tree languages and describe how these models can approximate any stochastic rational tree language. The model is applied to the task of learning a probabilistic k-testable model from a sample of parsed sentences. In particular, a parser for a natural language grammar that incorporates smoothing is shown.