Mobile genetic elements such as plasmids are important for the evolution of prokaryotes. It has been suggested that there are differences between functions coded for by mobile genes and those in the “core” genome and that these differences can be seen between plasmids and chromosomes. In particular, it has been suggested that essential genes, such as those involved in the formation of structural proteins or in basic metabolic functions, are rarely located on plasmids. We model competition between genotypically varying bacteria within a single population to investigate whether selection favors a chromosomal location for essential genes. We find that in general, chromosomal locations for essential genes are indeed favored. This is because the inheritance of chromosomes is more stable than that for plasmids. We define the “degradation” rate as the rate at which chance genetic processes, for example, mutation, deletion, or translocation, render essential genes nonfunctioning. The only way in which plasmids can be a location for functioning essential genes is if chromosomal genes degrade faster than plasmid genes. If the two degradation rates are equal, or if plasmid genes degrade faster than chromosomal genes, functioning essential genes will be found only on chromosomes.