We report a detection of the baryon acoustic oscillation (BAO) feature in the flux-correlation function of the Ly alpha forest of high-redshift quasars with a statistical significance of five standard deviations. The study uses 137 562 quasars in the redshift range 2.1 <= z <= 3.5 from the data release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-III. This sample contains three times the number of quasars used in previous studies. The measured position of the BAO peak determines the angular distance, D-A(Z = 2.34) and expansion rate, H(z = 2.34), both on a scale set by the sound horizon at the drag epoch, r(d). We find D-A/r(d) = 11.28 +/- 0.65(1 sigma)(-1.2)(+2.8)(2 sigma) and D-H/r(d) = 9.18 +/- 0.28(1 sigma) +/- 0.6(2 sigma) where D-H = c/H. The optimal combination, similar to(DHDA0.3)-D-0.7/r(d) is determined with a precision of similar to 2%. For the value r(d) = 147.4 Mpc, consistent with the cosmic microwave background power spectrum measured by Planck, we find D-A(Z = 2.34) = 1662 +/- 96(1 sigma) Mpc and H(z = 2.34) = 222 +/- 7(1 sigma) km s(-1) Mpc(-1). Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors. Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Ly alpha forest cross-correlation. The autocorrelation and cross-correlation approaches are complementary because of the quite different impact of redshift-space distortion on the two measurements. The combined constraints from the two correlation functions imply values of D-A/r(d) that are 7% lower and 7% higher for D-H/r(d) than the predictions of a flat ACDM cosmological model with the best-fit Planck parameters. With our estimated statistical errors, the significance of this discrepancy is approximate to 2.5 sigma.