Trypanosoma brucei is a parasitic protozoan that causes African sleeping sickness. It contains a flagellum required for locomotion and viability. In addition to a microtubular axoneme, the flagellum contains a crystalline paraflagellar rod (PFR) and connecting proteins. We show here, by cryoelectron tomography, the structure of the flagellum in three bending states. The PFR lattice in straight flagella repeats every 56 nm along the length of the axoneme, matching the spacing of the connecting proteins. During flagellar bending, the PFR crystallographic unit cell lengths remain constant while the interaxial angles vary, similar to a jackscrew. The axoneme drives the expansion and compression of the PFR lattice. We propose that the PFR modifies the in-plane axoneme motion to produce the characteristic trypanosome bihelical motility as captured by high-speed light microscope videography.