An approach is presented to calculate thermal boundary resistance in molecules, which occurs, for example, at the interfaces between moieties held at fixed temperatures and a molecular bridge that connects them. If the vibrational frequencies of each moiety lie outside of the band of heat-carrying modes of the bridge, anharmonic interactions mediate thermal conduction at the boundaries. We have expressed thermal boundary conductance in terms of the low-order anharmonic interactions between a moiety and a molecular bridge. Differences in the temperature-dependent boundary conductance at each end of the bridge can be exploited in the design of a molecular thermal diode. The approach is illustrated with the calculation of thermal boundary conductance and thermal rectification in azulene-(CH2)(N)-anthracene.