A new automated variance reduction method for the Monte Carlo simulation of multigroup neutron transport source-detector problems is described. The method is based on a modified transport problem that can be solved by analog Monte Carlo with zero variance. The implementation of this modified problem is impractical, in part because it requires the exact solution of an adjoint transport problem. The new local importance function transform (LIFT) method is developed to overcome this difficulty by approximating the exact adjoint solution with a piecewise-continuous function containing parameters that are obtained from a deterministic adjoint calculation. The transport and collision processes of the transformed Monte Carlo problem bias source distribution, distance to collision, and selection of postcollision energy groups and directions. A companion paper provides numerical results that demonstrate the efficiency of the LIFT method.