Crystallographic, magnetic, and NMR properties of a Na1CoO2 single crystal with x approximately = 1 are presented. We identify the stoichiometric Na1CoO2 phase, which is shown to be a nonmagnetic insulator, as expected for homogeneous planes of Co3+ ions with S = 0. In addition, we present evidence that, because of slight average Na deficiency, chemical and electronic phase separation leads to a segregation of Na vacancies into the well-defined, magnetic, Na0.8CoO2 phase. The importance of phase separation is discussed in the context of magnetic order for x approximately = 0.8 and the occurrence of a metal-insulator transition for x --> 1.