Long range ordering between chromium and thallium has been evidenced for the first time in copper oxychromate Tl3(CrO4)Sr8Cu4O16 using HREM, XRD and ND. This compound, which crystallizes in an orthorhombic cell with a = 3.7803(1) Å, b = 15.2573(2) Å and c = 17.6737(3) Å  derives from the "1201" TlSr2CuO5 structure by replacing one thallium oxygen polyhedra out of four by one CrO4 group in an ordered way. The Mayn features that characterize this original structure deal with the waving character of the [CuO2]∞ layers, and the absolute planar character of the [(Tl,Cr)O]∞ layers. In the [(Tl,Cr)O]∞ layers, the thallium and oxygen atoms form triple ribbons of edge-sharing TlO4 tetrahedra and TlO6 octahedra running along a, whereas the CrO4 tetrahedra are displayed in rows running along a, but are disconnected from each other and from the other polyhedra in the layer. Two kinds of CuO6 octahedra are observed, whose distortions originate from their connection with different polyhedra along c. This superconductor, whose Tc can be raised to 34 K after argon-hydrogen annealing, exhibits a rather high superconducting volume fraction (> 40%) compared to other "1201" thallium cuprates.