As I understand it, plasmids, like mitochondria, have their own genetic material and are capable of self-replication.
According to Wikipedia: Plasmids are considered replicons, units of DNA capable of replicating autonomously within a suitable host. However, like viruses, they are not classified as life. Plasmids are transmitted from one bacterium to another through conjugation. Unlike viruses, plasmids are "naked" DNA. However, some classes of plasmids encode the conjugative "sex" pilus necessary for their own transfer.
My understanding of that is that a bacteria gets their plasmids not because of the replication of their circular chromosome, nor because that chromosome have genes to code for the plasmid (I don't really know if that's possible), but because of the self-replication of their own plasmids.
So, my question is how the first plasmid got into the first bacteria, if they are not in their chromosomes? Were they a virus other prokaryotic cell that had circular DNA, and got phagocytosed by that bacteria ?