B chromosomes are additional, usually unstable constituents of the genome of many organisms. Their origin, however, is often unclear and their evolutionary relevance is not well understood. They may range from being deleterious to neutral or even beneficial. We have followed the genetic fate of B chromosomes in the asexual, all-female fish Poecilia formosa over eight generations. In this species, B chromosomes come in the form of one to three tiny microchromosomes derived from males of the host species that serve as sperm donors for this gynogenetic species. All microchromosomes have centromeric heterochromatin but usually only one has a telomere. Such microchromosomes are stably inherited, while the telomereless are prone to be lost in both the soma and germline. In some cases the stable microchromosome carries a functional gene lending support to the hypothesis that the B chromosomes in P. formosa could increase the genetic diversity of the clonal lineage in this ameiotic organism and to some degree counteract the genomic decay that is supposed to be connected with the lack of recombination.