We measure the imprint of primordial baryon acoustic oscillations (BAOs) in the correlation function of Ly α absorption in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS) in Data Release 14 (DR14) of the Sloan Digital Sky Survey (SDSS)-IV. In addition to 179 965 spectra with absorption in the Lyman- α (Ly α) region, we use Ly α absorption in the Lyman- β region of 56 154 spectra for the first time. We measure the Hubble distance, D H, and the comoving angular diameter distance, D M, relative to the sound horizon at the drag epoch r d at an effective redshift z = 2.34. Using a physical model of the correlation function outside the BAO peak, we find D H(2.34)/ r d = 8.86 ± 0.29 and D M(2.34)/ r d = 37.41 ± 1.86, within 1 σ from the flat-ΛCDM model consistent with CMB anisotropy measurements. With the addition of polynomial “broadband” terms, the results remain within one standard deviation of the CMB-inspired model. Combined with the quasar-Ly α cross-correlation measurement presented in a companion paper, the BAO measurements at z = 2.35 are within 1.7 σ of the predictions of this model.