  We formulate and solve the perhaps simplest two-body bound state problem for
interacting Dirac fermions in two spatial dimensions. A two-body bound state is
predicted for gapped graphene monolayers in the presence of weakly repulsive
electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where
the most interesting case corresponds to $Z=1$. We introduce a variational
Chandrasekhar-Dirac spinor wave function and show the existence of at least one
bound state. This state leaves clear signatures accessible by scanning
tunneling microscopy. One may thereby obtain direct information about the
strength of electron-electron interactions in graphene.
