The recently discovered iron arsenide superconductors appear to display a universal set of characteristic features, including proximity to a magnetically ordered state and robustness of the superconductivity in the presence of disorder. Here we show that superconductivity in Fe1+?Se, which can be considered the parent compound of the superconducting arsenide family, is destroyed by very small changes in stoichiometry. Further, we show that nonsuperconducting Fe1+?Se is not magnetically ordered down to 5 K. These results suggest that robust superconductivity and immediate instability against an ordered magnetic state should not be considered as intrinsic characteristics of iron-based superconducting systems.