Abstract: We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom, with potential defined by Gauss law. The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius R. In contrast to the case where the extra dimension is uncompactified, where for weak charges there are no bound states and for strong charges the atom is unstable, it has been found that the case with a compactified extra dimension is qualitatively different. We use a classical Hardy inequality, its local modification and the KLMN theorem to show that the hydrogen atom in a compactified universe is stable for a compactification radius smaller than a quarter of the Bohr radius.