We present a partial dependency parser for Irish. Constraint Grammar (CG) based rules are used to annotate dependency relations and grammatical functions. Chunking is performed using a regular-expression grammar which operates on the dependency tagged sentences. As this is the first implementation of a parser for unrestricted Irish text (to our knowledge), there were no guidelines or precedents available. Therefore deciding what constitutes a syntactic unit, and how it should be annotated, accounts for a major part of the early development effort. Currently, all tokens in a sentence are tagged for grammatical function and local dependency. Long-distance dependencies, prepositional attachments or coordination are not handled, resulting in a partial dependency analysis. Evaluations show that the partial dependency analysis achieves an f-score of 93.60% on development data and 94.28% on unseen test data, while the chunker achieves an f-score of 97.20% on development data and 93.50% on unseen test data.