Although compounds of the formula AMoO(2)F(3) (A = K, Rb, Cs, NH4, Tl) have been known for decades, crystal structures have only been reported for CsMoO2F3 and NH4MoO2F3. The three compounds (Rb/NH4/Tl)MoO2F3 are isostructural and crystallize in the centrosymmetric space group C2/c (No. 15). The compounds contain the MoO2F3- anionic chain, composed of corner-sharing MoO2F4 octahedra, with Mo6+ coordinated by two cis bridging fluoride anions that are trans to terminal oxide anions. The MoO2F3- chain has a very unusual and complex chain structure; a single chain contains alternating zig-zag and helical sections. These helical regions alternate in chirality along the chain, and thus the chains exhibit periodic tendril perversion. To the best of the authors' knowledge, no other materials with a similar chain structure have been reported. On the other hand, KMoO2F3 is noncentrosymmetric and chiral, crystallizing in the enantiomorphic space group P2(1)2(1)2(1) (No. 19). KMoO2F3 also contains the MoO2F3- anionic chain. However, the chain is helical, with only one enantiomer present, resulting in a chiral, noncentrosymmetric structure.