A limited quantum chemistry approach has been used to examine changes to the electric-field gradient at oxygen sites in rare-earth barium copper oxides (RBCO) due to a bonded muon (or hydrogen). Results are reported for an all electron, extended basis set calculation for an OMu− molecule which is embedded in various point charge clusters to simulate the RBCO crystal environment. Differences between the gradients for O2− and OMu− are examined for five likely muon bond sites. In each case the muon significantly modifies the calculated gradient.