Aim: There are several competing hypotheses to explain the high species richness of the Indo-Australian Archipelago (IAA) marine biodiversity hotspot centred within Southeast (SE) Asia. We use phylogenetic methods to provide a novel perspective on this problem using viviparous sea snakes, a group with high species richness in the IAA that is highly distinct from other taxa previously studied, both phylogenetically (Reptilia, Amniota) and biologically (e.g.viviparity and direct development). Location: Indian Ocean and the West Pacific. Methods: We used likelihood and Bayesian methods to reconstruct a multi-locus time-calibrated phylogeny for c.70% of viviparous sea snake species, many sampled from multiple localities in Australasia, Southeast Asia and the Indian Ocean. We then compared rates and temporal concordance of inferred vicariance and dispersal events between marine basins using several approaches including new Bayesian analyses that allow for clade-specific and event-specific dispersal rates. Results: Phylogenetic analyses and novel Bayesian biogeographical reconstructions indicate that viviparous sea snakes underwent rapid speciation after colonizing SE Asia c.3 million years ago. Most of the SE Asian sea snake diversity is the result of insitu speciation, most consistent with the 'centre of origin' and 'centre of refuge' models for biodiversity hotspots. There is also speciation at the periphery, or entirely outside SE Asia; however, contrary to predictions of the 'accumulation' and 'overlap' models, these new outlying taxa do not preferentially disperse back into SE Asia. Instead, lineages are equally likely to disperse either into or away from SE Asia. Main conclusion: The high diversity of sea snakes in SE Asia (and hence the IAA) is mostly explained by insitu speciation rather than accumulation or overlap. Most speciation events are contemporaneous with sea level changes that generated and dissolved barriers between marine basins during the last 2.5 million years.