We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2 × 1:H surface. Room temperature, ultrahigh vacuum tunneling spectroscopy measurements of nanometer-sized single layer graphene reveal a size-dependent energy gap ranging from 0.1 to 1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunneling microscopy topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.