Our Local Group of galaxies is moving with respect to the cosmic microwave background (CMB) with a velocity1 of V CMB = 631 ± 20 km s−1 and participates in a bulk flow that extends out to distances of ~20,000 km s−1 or more2–4. There has been an implicit assumption that overabundances of galaxies induce the Local Group motion5–7. Yet underdense regions push as much as overdensities attract8, but they are deficient in light and consequently difficult to chart. It was suggested a decade ago that an underdensity in the northern hemisphere roughly 15,000 km s−1 away contributes significantly to the observed flow9. We show here that repulsion from an underdensity is important and that the dominant influences causing the observed flow are a single attractor — associated with the Shapley concentration — and a single previously unidentified repeller, which contribute roughly equally to the CMB dipole. The bulk flow is closely anti-aligned with the repeller out to 16,000 ± 4,500 km s−1. This ‘dipole repeller’ is predicted to be associated with a void in the distribution of galaxies.