Stem cell banking is a complex and controversial subject. There are currently three private stem cell banks in South Africa. At present, South Africa does not have a public stem cell bank. The de facto legal vacuum in which the private banks have operated thus far will change at some point in the future following the publication, for public comment, of draft regulations relating to human stem cells in the Government Gazette. If promulgated in their present form, the draft regulations would effectively ban private stem cell banking. We argue that such a ban would constitute an unjustifiable violation of at least four constitutionally protected rights, namely, the right to access to health care, the right to bodily integrity, children's rights, and the right to freedom of economic activity. The traditional arguments against private banking that are based on the low recall rate of banked cells, and the diversion of resources away from public banks, may justify the regulation of private banks, but not their prohibition. Specific attention is given to the argument against private banking that is purportedly based on equality. This argument is shown to be based on an incorrect conception of equality, namely that equality justifies 'levelling down', in which unequal access to a certain social good can justifiably be remedied by denying everyone access to this social good. Less restrictive measures are proposed to regulate stem cell banking in South Africa for the public good and in a constitutionally acceptable fashion.