This paper presents a probabilistic extension of Discontinuous Phrase Structure Grammar (DPSG), a formalism designed to describe discontinuous constituency phenomena adequately and perspicuously by means of trees with crossing branches. We outline an implementation of an agenda-based chart parsing algorithm that is capable of computing the Most Probable Parse for a given input sentence for probabilistic versions of both DPSG and Context-Free Grammar. Experiments were conducted with both types of grammars extracted from the NEGRA corpus. In spite of the much greater complexity of DPSG parsing in terms of the number of (partial) analyses that can be constructed for an input sentence, accuracy results from both experiments are comparable. We also briefly hint at future lines of research aimed at more efficient ways of probabilistic parsing with discontinuous constituents.