We report the detection of repeat bursts from the source of FRB 171019, one of the brightest fast radio bursts (FRBs) detected in the Australian Square Kilometre Array Pathfinder (ASKAP) fly’s eye survey. Two bursts from the source were detected with the Green Bank Telescope in observations centered at 820 MHz. The repetitions are a factor of ∼590 fainter than the ASKAP-discovered burst. All three bursts from this source show no evidence of scattering and have consistent pulse widths. The pulse spectra show modulation that could be evidence for either steep spectra or patchy emission. The two repetitions were the only ones found in an observing campaign for this FRB totaling 1000 hr, which also included ASKAP and the 64 m Parkes radio telescope, over a range of frequencies (720─2000 MHz) at epochs spanning two years. The inferred scaling of repetition rate with fluence of this source agrees with the other repeating source, FRB 121102. The detection of faint pulses from FRB 171019 shows that at least some FRBs selected from bright samples will repeat if follow-up observations are conducted with more sensitive telescopes.