We measure the quasar two-point correlation function over the redshift range 2.2 < z < 2.8 using data from the Baryon Oscillation Spectroscopic Survey. We use a homogeneous subset of the data consisting of 27 129 quasars with spectroscopic redshifts – by far the largest such sample used for clustering measurements at these redshifts to date. The sample covers 3600 deg2, corresponding to a comoving volume of 9.7 (h−1 Gpc)3 assuming a fiducial Λ cold dark matter cosmology, and it has a median absolute i-band magnitude of −26, k-corrected to z= 2. After accounting for redshift errors we find that the redshift-space correlation function is fitted well by a power law of slope −2 and amplitude s0= (9.7 ± 0.5) h−1 Mpc over the range 3 < s < 25 h−1 Mpc. The projected correlation function, which integrates out the effects of peculiar velocities and redshift errors, is fitted well by a power law of slope −1 and r0= (8.4 ± 0.6) h−1 Mpc over the range 4 < R < 16 h−1 Mpc. There is no evidence for strong luminosity or redshift dependence to the clustering amplitude, in part because of the limited dynamic range in our sample. Our results are consistent with, but more precise than, previous measurements at similar redshifts. Our measurement of the quasar clustering amplitude implies a bias factor of b≃ 3.5 for our quasar sample. We compare the data to models to constrain the manner in which quasars occupy dark matter haloes at z∼ 2.4 and infer that such quasars inhabit haloes with a characteristic mass of 〈M〉≃ 1012 h−1 M⊙ with a duty cycle for the quasar activity of 1 per cent.