Morphological segmentation breaks words into morphemes (the basic semantic units). It is a key component for natural language processing systems. Unsupervised morphological segmentation is attractive, because in every language there are virtually unlimited supplies of text, but very few labeled resources. However, most existing model-based systems for unsupervised morphological segmentation use directed generative models, making it difficult to leverage arbitrary overlapping features that are potentially helpful to learning. In this paper, we present the first log-linear model for unsupervised morphological segmentation. Our model uses overlapping features such as morphemes and their contexts, and incorporates exponential priors inspired by the minimum description length (MDL) principle. We present efficient algorithms for learning and inference by combining contrastive estimation with sampling. Our system, based on monolingual features only, outperforms a state-of-the-art system by a large margin, even when the latter uses bilingual information such as phrasal alignment and phonetic correspondence. On the Arabic Penn Treebank, our system reduces F1 error by 11% compared to Morfessor.