For intermediate sized chemical systems the use of an auxiliary basis set (ABS) to fit the charge density provides a useful means of accelerating the performance of various quantum chemical methods. As a consequence much effort has been devoted to the design of various ABSs. This paper explores a fundamentally new approach where the ABS is created dynamically based on the specific orbital basis set (OBS) being used. The new approach includes a parameter that is used to coalesce candidate fitting functions together but which can also be used to provide some coarse grain control over the number of functions in the ABS. The accuracy of the new automatically generated ABS (auto-ABS) is systemically studied for a variety of small systems containing the elements H-Kr. Errors in the Coulomb energy computed using auto-ABS and with a variety of OBSs are shown to be small compared to errors in the Hartree-Fock energy due to incompleteness in the OBS. In contrast to fixed size ABSs, the use of auto-ABS is shown to lead to smaller errors as the size (quality) of the OBS is expanded. The performance of auto-ABS is also compared with the use of the recently proposed universal fitting sets [Weigend, Phys. Chem. Chem. Phys. 8, 1057 (2006)] for 180 compounds containing atoms from H to Kr.