The paper introduces an ongoing project for the development of a parallel treebank for Italian, English and French, i.e. Parallel--TUT, or simply ParTUT. For the development of this resource, both the dependency and constituency-based formats of the Italian Turin University Treebank (TUT) have been applied to a preliminary dataset, which includes the whole text of the Universal Declaration of Human Rights, and sentences from the JRC-Acquis Multilingual Parallel Corpus and the Creative Commons licence. The focus of the project is mainly on the quality of the annotation and the investigation of some issues related to the alignment of data that can be allowed by the TUT formats, also taking into account the availability of conversion tools for display data in standard ways, such as Tiger--XML and CoNLL formats. It is, in fact, our belief that increasing the portability of our treebank could give us the opportunity to access resources and tools provided by other research groups, especially at this stage of the project, where no particular tool -- compatible with the TUT format -- is available in order to tackle the alignment problems.