The discovery of non-zero neutrino masses has introduced a new mass scale into the Standard Model of particle physics that is at least six orders of magnitude below the electron mass. In the absence of a Standard Model mechanism that can explain the origin of the neutrino mass scale, one can consider the possibility that neutrinos are Majorana fermions which would allow right-handed neutrinos to acquire an additional mass term without requiring new interactions. A mixing of the neutrino Majorana mass terms and Standard Model Dirac mass terms generates mass eigenstates corresponding to light neutrinos, which have already been observed, and heavy neutrinos, which have not. This thesis presents a search for same-sign lepton pairs from the decay of heavy Majorana neutrinos produced in sqrt(s)=8 TeV proton-proton collisions in the ATLAS detector at the CERN Large Hadron Collider, using data corresponding to an integrated luminosity of 20.3 fb^(-1). No excess of events above the expected background is observed and 95% confidence level upper limits are set on the cross-section times branching ratio with respect to heavy Majorana neutrino masses in the range 100 to 500 GeV. The presented limits are the most stringent direct limits set to date for heavy neutrino masses greater than 100 GeV.