All algae with chloroplasts located not freely in the cytosol, but inside two extra membranes, probably arose chimerically by the permanent fusion of two different eukaryote cells: a protozoan host and a eukaryotic algal symbiont. Two such groups, cryptomonads (phylum Cryptista) and Chlorarachniophyta, still retain a DNA-containing relic of the nucleus of the algal endosymbiont, known as the nucleomorph, as well as the host nucleus. These two phyla were traditionally assumed to have obtained their chloroplasts separately by two independent symbioses. We have sequenced the nuclear and the nucleomorph 18S rRNA genes of the nonphotosynthetic cryptomonad Chilomonas paramecium. Our phylogenetic analysis suggests that cryptomonad and chlorarachniophyte nucleomorphs may be related to each other and raises the possibility that both phyla may have diverged from a common ancestral chimeric cell that originated by a single endosymbiosis involving an algal endosymbiont related to the ancestor of red algae. But, because of the instability of the molecular trees when different taxa are added, there is insufficient evidence to overturn the traditional view that Chlorarachnion nucleomorphs evolved separately from a relative of green algae. The four phyla that contain chromophyte algae (those with chlorophyll c--i.e., Cryptista, Heterokonta, Haptophyta, Dinozoa) are distantly related to each other and to Chlorarachniophyta on our trees. However, all of the photosynthetic taxa within each of these four phyla radiate from each other very substantially after the radiation of the four phyla themselves. This favors the view that the common ancestor of these four phyla was not photosynthetic and that chloroplasts were implanted separately into each much more recently. This probable polyphyly of the chromophyte algae, if confirmed, would make it desirable to treat Cryptista, Heterokonta, and Haptophyta as separate kingdoms, rather than to group them together in the single kingdom Chromista.