Individuals with autism spectrum disorder demonstrate narrative (i.e. storytelling) difficulties which can significantly impact their ability to form and maintain social relationships. However, existing research has not comprehensively documented these impairments in more open-ended, emotionally evocative situations common to daily interactions. Computational linguistic measures offer a promising complement to traditional hand-coding methods of narrative analysis and in this study were applied together with hand coding of narratives elicited with emotionally salient scenes from the Thematic Apperception Test. In total, 19 individuals with autism spectrum disorder and 14 typically developing controls were asked to tell stories about six images from the Thematic Apperception Test. Both structural and qualitative aspects of narrative were assessed using a hand-coding system and Latent Semantic Analysis, an automated computational measure of semantic similarity. Individuals with autism spectrum disorder demonstrated significant difficulties with the use of complex syntax to integrate their narratives and problems explaining characters' intentions. These and other key narrative skills were strongly related to narrative competence scores derived from Latent Semantic Analysis, which also distinguished the autism spectrum disorder group from controls. Together, results underscore key narrative impairments in autism spectrum disorder and support the promise of Latent Semantic Analysis as a valuable tool for the quantitative assessment of complex language abilities.