We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-α flux fluctuations at a redshift zeff = 2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of error covariance matrix estimation) and is consistent with predictions of the standard ΛCDM model. We assess the biases in our method, stability of the error covariance matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100 × (αiso - 1) = -1.6+2.0 +4.3 +7.4-2.0 -4.1 -6.8 (stat.) ±1.0 (syst.) (multiple statistical errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat ΛCDM with Ωm = 0.27, h = 0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100 × (α|| - 1) = -1.3+3.5 +7.6 +12.3-3.3 -6.7 -10.2 (stat.) ±2.0 (syst.) and 100 × (α⊥ - 1) = -2.2+7.4 +17-7.1 -15 (stat.) ±3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ~ -0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-α sample, providing an important consistency test of the standard cosmological model in a new redshift regime.