Some plant families show a striking imbalance in species diversity between the Neotropics and the Palaeotropics. The woody plant family Chrysobalanaceae is a typical example of this pattern, with 80% of the 531 species in the Neotropics. In order to test alternative interpretations for this pattern, we generated a dated phylogenetic hypothesis for Chrysobalanaceae, using DNA sequence data from one nuclear and six plastid markers. Using a maximum likelihood approach, we jointly inferred ancestral areas and diversification rates in the Neotropics and Palaeotropics. We found that Chrysobalanaceae most probably originated in the Palaeotropics about 80 Mya. The family dispersed into the Neotropics at least four times beginning 40–60 Mya, with at least one back-dispersal to the Palaeotropics. Members of Chrysobalanaceae have experienced higher extinction, speciation and net diversification rates in the Neotropics. Hence, the high species diversity of Chrysobalanaceae in the Neotropics appears to be primarily caused by a higher speciation rate in this region. Several recent studies have shown high diversification rates in Neotropical plant families, but have focused on Andean-centred taxa. Ours is the first study to find a similar pattern in a family for which the centre of diversity is in eastern and central Amazonia.