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We present a measurement of the baryon acoustic oscillation (BAO) scale atredshift $z=2.35$ from the three-dimensional correlation of Lyman-$\alpha$(Ly$\alpha$) forest absorption and quasars. The study uses 266,590 quasars inthe redshift range $1.77<z<3.5$ from the Sloan Digital Sky Survey (SDSS) DataRelease 14 (DR14). The sample includes the first two years of observations bythe SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS), providingnew quasars and re-observations of BOSS quasars for improved statisticalprecision. Statistics are further improved by including Ly$\alpha$ absorptionoccurring in the Ly$\beta$ wavelength band of the spectra. From the measuredBAO peak position along and across the line of sight, we determined the Hubbledistance $D_{H}$ and the comoving angular diameter distance $D_{M}$ relative tothe sound horizon at the drag epoch $r_{d}$: $D_{H}(z=2.35)/r_{d}=9.20\pm 0.36$and $D_{M}(z=2.35)/r_{d}=36.3\pm 1.8$. These results are consistent at$1.5\sigma$ with the prediction of the best-fit spatially-flat cosmologicalmodel with the cosmological constant reported for the Planck (2016) analysis ofcosmic microwave background anisotropies. Combined with the Ly$\alpha$auto-correlation measurement presented in a companion paper, the BAOmeasurements at $z=2.34$ are within $1.7\sigma$ of the predictions of thismodel.

Baryon acoustic oscillations from the cross-correlation of Ly$\alpha$ absorption and quasars in eBOSS DR14