Recent suggestions that endosymbionts in a diatom and an amoeba represent independent origins of plastids from those in plants and algae raise again the question of how many times plastids have evolved. In this Opinion article, we review the evidence for a single origin or multiple origins of primary plastids. Although the data are widely taken as supporting a single origin, we stress the assumptions underlying that view, and argue for a more cautious interpretation. We also suggest that the implicit view of plastids being acquired from single ancestors at a single point (or points) in time is an over-simplification.