Three Monte Carlo methods for computing transition dipole moments are presented. Two of these approaches are based on the use of multiple Monte Carlo ‘‘random walks’’ to sample different probability distributions. The remaining technique employs a single Monte Carlo walk and averages an analytic approximation to the Green’s function to sample other distributions. The accuracy and efficiency of each method is investigated by computing the transition dipole moment between the 1s and 2px states of the hydrogen atom. Monte Carlo parameters, such as the time step size and the convergence time, are varied in order to study their effect on computed results. It is found that the approach based on a guided Metropolis walk with quantum Monte Carlo ‘‘side walks’’ and also the approach based on Green’s function averages yield accurate transition dipole moments efficiently. These two methods also yield accurate energies and expectation values for the individual eigenstates. The approach based on two equivalent quantum Monte Carlo walks, one for each state, is found to be least satisfactory.