The Roche lobe formalism describes mass transfer from one star to another. We develop an extension to hierarchical triples, considering the case in which a star donates mass to a companion which is itself a binary. The L1 point moves as the inner binary rotates, and the Roche lobe pulsates with the period of the inner binary. Signatures of mass transfer may therefore be imprinted with the orbital period of the inner binary. For some system parameters, the pulsing Roche lobe can drive mass transfer at high rates. Systems undergoing this type of mass transfer include those with inner binaries consisting of compact objects that will eventually merge, as well as progenitors of Type Ia supernovae.
