Electrons in two-dimensional graphene sheets behave as interacting chiral Dirac fermions and have unique screening properties due to their symmetry and reduced dimensionality. By using a combination of scanning tunneling spectroscopy measurements and theoretical modeling we have characterized how graphene's massless charge carriers screen individual charged calcium atoms. A backgated graphene device configuration has allowed us to directly visualize how the screening length for this system can be tuned with carrier density. Our results provide insight into electron-impurity and electron-electron interactions in a relativistic setting with important consequences for other graphene-based electronic devices.