A new chromium tellurite oxochloride, Cr3Te5O13Cl3, has been prepared by solid-state reaction and the crystal structure was determined by single crystal X-ray diffraction. The compound crystallizes in the non-centrosymmetric space group P2(1)2(1)2(1) with the unit cell a = 4.90180(10) Å, b = 17.3394(2) Å, c = 17.5405(2) Å, Z = 4, R1 = 0.0282. The Cr(3+) ions have octahedral [CrO6] oxygen coordination, the Te(4+) ions have one sided [TeO3] and [TeO3Cl] coordinations. The [CrO6] octahedra are edge sharing and form chains extending along [100]. These are connected by corner sharing [TeO3] and [TeO3Cl] groups to form layers parallel to (110). The layers are connected by weak interactions in between Te(4+) in the layers and Cl(-) ions located in between. The compound undergoes antiferromagnetic ordering at ~34 K with a Weiss constant of -230 K. Isothermal magnetization measurements reveal a critical field of about 0.25 T above which the magnetization versus field changes from linear to a Brillouin-like saturation behaviour. The frustration ratio amounts to ~6.8 indicative of sizable competing antiferromagnetic spin-exchange interaction. The dielectric constant ε (6 kHz) amounts to ~7.9 and decreases by about 1% on cooling from 50 K to liquid helium temperatures.