The magnetic properties and the low-temperature nuclear and magnetic structures of Cu3Mo2O9 are reported. It consists of magnetic chains of oxygen-bridged vertex-shared Cu-4 tetrahedra connected into a 3D network by bridging MoO4. Each chain is a segment of the pyrochlore structure. The magnetic properties are dominated by anti-ferromagnetic coupling and show a low-dimensional behavior with a broad maximum at 20 K. At 9.5 K, long-range antiferromagnetic ordering with a small canting is observed. The magnetic structure determination from neutron diffraction resolves only the orientations and magnitude (1.0(1) mu(B) per Cu) of the moments of two of the three crystallographically independent atoms. The third appears not to contribute to the long-range ordering. Geometric frustration may be responsible for the randomness. It is a unique antiferromagnet with eight sublattices (two sets of four) in the ac plane, leaving the canting to be only possible along the b axis.