The origin of species diversity has challenged biologists for over two centuries. Allopatric speciation, the divergence of species resulting from geographical isolation, is well documented. However, sympatric speciation, divergence without geographical isolation, is highly controversial. Claims of sympatric speciation must demonstrate species sympatry, sister relationships, reproductive isolation, and that an earlier allopatric phase is highly unlikely. Here we provide clear support for sympatric speciation in a case study of two species of palm (Arecaceae) on an oceanic island. A large dated phylogenetic tree shows that the two species of Howea, endemic to the remote Lord Howe Island, are sister taxa and diverged from each other well after the island was formed 6.9 million years ago. During fieldwork, we found a substantial disjunction in flowering time that is correlated with soil preference. In addition, a genome scan indicates that few genetic loci are more divergent between the two species than expected under neutrality, a finding consistent with models of sympatric speciation involving disruptive/divergent selection. This case study of sympatric speciation in plants provides an opportunity for refining theoretical models on the origin of species, and new impetus for exploring putative plant and animal examples on oceanic islands.