We report observations of very large amplitude whistler mode waves in the Earth's nightside inner radiation belt enabled by the STEREO Time Domain Sampler. Amplitudes range from 30-110 mV/m (zero-peak), 2 to 3 orders of magnitude larger than previously observed in this region. Measurements from the peak electric field detector (TDSMax) indicate that these large-amplitude waves are prevalent throughout the plasmasphere. A detailed examination of high time resolution electric field waveforms is undertaken on a subset of these whistlers at L < 2, associated with pump waves from lightning flashes and the naval transmitter NPM in Hawaii, that become unstable after propagation through the ionosphere and grow to large amplitudes. Many of the waveforms undergo periodic polarization reversals near the lower hybrid and NPM naval transmitter frequencies. The reversals may be related to finite plasma temperature and gradients in density induced by ion cyclotron heating of the plasma at 200 Hz, the modulation frequency of the continuous-mode NPM naval transmitter signal. Test particle simulations using the amplitudes and durations of the waves observed herein suggest that they can interact strongly with high-energy (>100 keV) electrons on a time scale of <1 s and thus may be an important previously unaccounted for source of energization or pitch-angle scattering in the inner radiation belt.