Nearby `open' clusters of stars (those that are not gravitationally bound) have played a crucial role in the development of stellar astronomy because, as a consequence of the stars having a common age, they provide excellent natural laboratories to test theoretical stellar models. Clusters also play a fundamental part in determining distance scales. The satellite Hipparcos surprisingly found that an extensively studied open cluster-the Pleiades (also known as the Seven Sisters)-had a distance of D = 118 +/- 4pc (refs 2, 3), about ten per cent smaller than the accepted value. The discrepancy generated a spirited debate because the implication was that either current stellar models were incorrect by a surprising amount or Hipparcos was giving incorrect distances. Here we report the orbital parameters of the bright double star Atlas in the Pleiades, using long-baseline optical/infrared interferometry. From the data we derive a firm lower bound of D > 127pc, with the most likely range being 133 < D < 137pc. Our result reaffirms the fidelity of current stellar models.