  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 $2.1\le z \le 3.5$ 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
$D_A/r_d=11.28\pm0.65(1\sigma)^{+2.8}_{-1.2}(2\sigma)$ and
$D_H/r_d=9.18\pm0.28(1\sigma)\pm0.6(2\sigma)$ where $D_H=c/H$. The optimal
combination, $\sim D_H^{0.7}D_A^{0.3}/r_d$ is determined with a precision of
$\sim2\%$. For the value $r_d=147.4~{\rm Mpc}$, consistent with the CMB power
spectrum measured by Planck, we find $D_A(z=2.34)=1662\pm96(1\sigma)~{\rm Mpc}$
and $H(z=2.34)=222\pm7(1\sigma)~{\rm km\,s^{-1}Mpc^{-1}}$. 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 auto-correlation 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 $D_A/r_d$ and
$D_H/r_d$ that are, respectively, 7% low and 7% high compared to the
predictions of a flat $\Lambda$CDM cosmological model with the best-fit Planck
parameters. With our estimated statistical errors, the significance of this
discrepancy is $\approx 2.5\sigma$.
