Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141-6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observed a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring (LT) precession of the orbit resulting from rapid rotation of the WD. LT precession. an effect of relativistic frame dragging, is a prediction of general relativity. This detection is consistent with an evolutionary scenario in which the WD accreted matter from the pulsar progenitor, spinning up the WD to a period of <200 seconds.