Cosmic rays are atomic nuclei arriving from outer space that reach the highest energies observed in nature. Clues to their origin come from studying the distribution of their arrival directions. Using $3 times 10^4$ cosmic rays above $8 times 10^{18}$ electron volts, recorded with the Pierre Auger Observatory from a total exposure of 76,800 square kilometers steradian year, we report an anisotropy in the arrival directions. The anisotropy, detected at more than the 5.2$sigma$ level of significance, can be described by a dipole with an amplitude of $6.5_{-0.9}^{+1.3}$% towards right ascension $alpha_{d} = 100 pm 10$ degrees and declination $delta_{d} = -24_{-13}^{+12}$ degrees. That direction indicates an extragalactic origin for these ultra-high energy particles.
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