Most photosynthetic dinoflagellates harbour the peridinin plastid. This plastid is surrounded by three membranes and its characteristic pigments are chlorophyll c and the carotenoid peridinin. The evolutionary origin of this peculiar plastid remains controversial and is hotly debated. On the recently published tree of concatenated plastid-encoded proteins, dinoflagellates emerge from within the Chromista (clade containing cryptophytes, heterokonts, and haptophytes) and cluster specifically with Heterokonta. These data inspired a new version of the 'chromalveolate' model, according to which the peridinin plastid evolved by 'descent with modification' from a heterokont-like plastid that had been acquired from a rhodophyte by an ancestral chromalveolate. However, this model of plastid evolution encounters serious obstacles. Firstly, the heterokont plastid is surrounded by four membranes, which means that the ancestral peridinin plastid must have lost one of these primary membranes. However, such a loss could be traumatic, because it could potentially disturb protein import into and/or within the plastid. Secondly, on the phylogenetic tree of Dinoflagellata and Heterokonta, the first to diverge are not plastid, but heterotrophic, aplastidal taxa. Thus, when accepting the single origin of the heterokont and peridinin plastids, we would have to postulate multiple plastid losses, but such a scenario is highly doubtful when the numerous non-photosynthetic functions of plastids and their existence in heterotrophic protists, including parasitic lineages, are considered. Taking these obstacles into account, we suggest an alternative interpretation of the concatenated tree of plastid-encoded proteins. According to our hypothesis, the peridinin plastid evolved from a heterokont alga through tertiary endosymbiosis.