Dinoflagellates are algae of tremendous importance to ecosystems and to public health. The cell biology and genome organisation of dinoflagellate species is highly unusual. For example, the plastid genomes of peridinin-containing dinoflagellates encode only a minimal number of genes arranged on small elements termed "minicircles". Previous studies of peridinin plastid genes have found evidence for divergent sequence evolution, including extensive substitutions, novel insertions and deletions, and use of alternative translation initiation codons. Understanding the extent of this divergent evolution has been hampered by the lack of characterised peridinin plastid sequences. We have identified over 300 previously unannotated peridinin plastid mRNAs from published transcriptome projects, vastly increasing the number of sequences available. Using these data, we have produced a well-resolved phylogeny of peridinin plastid lineages, which uncovers several novel relationships within the dinoflagellates. This enables us to define changes to plastid sequences that occurred early in dinoflagellate evolution, and that have contributed to the subsequent diversification of individual dinoflagellate clades. We find that the origin of the peridinin dinoflagellates was specifically accompanied by elevations both in the overall number of substitutions that occurred on plastid sequences, and in the Ka/Ks ratio associated with plastid sequences, consistent with changes in selective pressure. These substitutions, alongside other changes, have accumulated progressively in individual peridinin plastid lineages. Throughout our entire dataset, we identify a persistent bias towards non-synonymous substitutions occurring on sequences encoding photosystem I subunits and stromal regions of peridinin plastid proteins, which may have underpinned the evolution of this unusual organelle.