The intrinsic doping level of graphene prepared by mechanical exfoliation and standard lithography procedures on thermally oxidized silicon varies significantly and seems to depend strongly on processing details and the substrate morphology. Moreover, transport properties of such graphene devices suffer from hysteretic behavior under ambient conditions. The hysteresis presumably originates from dipolar adsorbates on the substrate or graphene surface. Here, we demonstrate that it is possible to reliably obtain low intrinsic doping levels and to strongly suppress hysteretic behavior even in ambient air by depositing graphene on top of a thin, hydrophobic self-assembled layer of hexamethyldisilazane (HMDS). The HMDS serves as a reproducible template that prevents the adsorption of dipolar substances. It may also screen the influence of substrate deficiencies.