We report on synthesis of single crystals of BaFe2Se3 and study of their crystal and magnetic structures by means of synchrotron single crystal X-ray and neutron powder diffraction. The crystal structure has orthorhombic symmetry and consists of double chains of FeSe4 edge connected tetrahedra intercalated by barium. Below 240 K long range block-spin checkerboard antiferromagnetic (AFM) order is developed. The magnetic structure is similar to one observed in A0.8Fe1.6Se2 (A=K, Rb or Cs) superconductors. The crystals exhibit a transition to the diamagnetic state with an onset transition temperature of Tc ~11 K. Though we observe FeSe as an impurity phase (<0.8% mass fraction) the diamagnetism unlikely can be attributed to the FeSe-superconductor which has Tc\approx8.5K.