Abstract: The last decade has seen two significant phenomena emerge in research communication: the rise of open access (OA) publishing, and the easy availability of evidence of online sharing in the form of altmetrics. There has been limited examination of the effect of OA on online sharing for journal articles, and little for books. This paper examines the altmetrics of a set of 32,222 books (of which 5% are OA) and a set of 220,527 chapters (of which 7% are OA) indexed by the scholarly database Dimensions in the Social Sciences and Humanities. Both OA books and chapters have significantly higher use on social networks, higher coverage in the mass media and blogs, and evidence of higher rates of social impact in policy documents. OA chapters have higher rates of coverage on Wikipedia than their non-OA equivalents, and are more likely to be shared on Mendeley. Even within the Humanities and Social Sciences, disciplinary differences in altmetric activity are evident. The effect is confirmed for chapters, although sampling issues prevent the strong conclusion that OA facilitates extra attention at the whole book level, the apparent OA altmetrics advantage suggests that the move towards OA is increasing social sharing and broader impact.