We measure the imprint of primordial baryon acoustic oscillations (BAOs) in the correlation function of Lyα 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 (Lyα) region, we use Lyα absorption in the Lyman-β region of 56 154 spectra for the first time. We measure the Hubble distance, D H , and the

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... ving 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 1σ 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-Lyα cross-correlation measurement presented in a companion paper, the BAO measurements at z = 2.35 are within 1.7σ of the predictions of this model.