A continuous-energy Monte Carlo method is developed to compute adjoint-based k-eigenvalue sensitivity coefficients with respect to nuclear data. The method is implemented into MCNP6 and is based upon similar methodologies used to compute other adjoint-weighted quantities. The Monte Carlo tallies employed are explained. Verification of the method is performed by comparing results to analytic solutions, direct density perturbations, and those from other software packages such as TSUNAMI-3D and MONK. Results of analytic solutions agree within a few tenths of a percent. Direct density perturbations and comparisons with other software generally agree within a few percent.