This paper presents the foundations, procedures, tests and first results of a dependency treebank of the Spanish Sign Language (LSE). Dependency syntax offers many advantages over other alternatives for the systematic and exhaustive syntactic analysis of a corpus. Nevertheless, the visual modality that is characteristic of sign languages poses unique challenges for their syntactic analysis, among which the most prominent is the simultaneity of expression: both hands, face and other non-manual components. Taking into account these and other particularities of sign languages, the paper explores the main difficulties faced when one tries to apply some usual categories and relations from the syntactic analysis of spoken and written languages to LSE.