We describe the first effort to annotate a signed language with syntactic dependency structure: the Swedish Sign Language portion of the Universal Dependencies treebanks.The visual modality presents some unique challenges in analysis and annotation, such as the possibility of both hands articulating separate signs simultaneously, which has implications for the concept of projectivity in dependency grammars.Our data is sourced from the Swedish Sign Language Corpus, and if used in conjunction these resources contain very richly annotated data: dependency structure and parts of speech, video recordings, signer metadata, and since the whole material is also translated into Swedish the corpus is also a parallel text.