In this paper, we propose a generic method for the detection of line segments in SAR images. The approach relies on an a contrario framework and is inspired by the state-of-the art LSD detector. As with all a contrario approaches, false detections are controlled through the use of a background model, whose development is especially challenging in the framework of SAR images. Indeed, statistical characteristics of SAR images strongly differ from those of optical images, making the use of existing background models intrinsically inadequate. In order to circumvent this problem, we proceed in two steps. First, the building blocks of the detector, namely the local orientations, are computed carefully to avoid any spatial bias. Second, we propose a new background model, in which the spatial dependency between local orientations are modeled with a Markov chain. This is in strong contrast with most existing a contrario methods who heavily rely on independence assumptions. We provide a complete and detailed algorithm for our line segment detector, and perform experiments on synthetic and real images demonstrating its efficiency. The source code of LSDSAR can be found in https://github.com/ChenguangTelecom/LSDSAR