A new cyano-bridged Tb(III)-Cr(III) heterometallic complex [Tb(H(2)O)(2)(DMF)(4){Cr(CN)(6)}]·H(2)O (DMF = dimethylformamide) (1), assembled from paramagnetic hexacyanochromium(III) [Cr(CN)(6)](3-) building block and highly anisotropic terbium(III) ion has been prepared and structurally and magnetically characterized. Complex 1 shows one-dimensional (1D) zig-zag chain-like structural motif which is further extended into three-dimensional network through hydrogen-bonding interactions. The long-range magnetic ordering observed in complex 1, which is possibly due to interchain magnetic dipolar interactions, illuminates that this complex is a molecule-based magnet with critical temperature of about 5 K. This higher critical temperature among those of Ln(III)-Cr(III) heterometallic complexes exhibiting long-range magnetic ordering is probably due to the introduction of highly anisotropic terbium(III) ion.