A new chiral 6:7 open-framework uranyl molybdate, [C₆H ₁₆N]₂[UO₂)₆(MoO₄) ₇(H₂O)₂)(H₂O)₂), has been synthesized by hydrothermal methods. The structure has been refined using single-crystal X-ray diffraction data collected at 20 and -127°C. The 20°C structure [orthorhombic, C222₁; a = 11.3045(14), b = 19.962(6), c = 24.416(5)Å, V = 5510(2)ų] has been refined to R₁ = 0.046 on the basis of 6093 unique observed reflections. The -127°C structure [orthorhombic, P2₁2 ₁2₁, a = 11.211(4), b= 19.880(10), c = 24.421(8) Å, V= 5443(4)ų] has been refined to R₁ = 0.047 on the basis of 6951 unique observed reflections. The structures are based upon topologically identical frameworks of corner-sharing UO₇ pentagonal bipyramids and MoO₄ tetrahedra. The extra-framework H₂O groups and protonated triethylamine molecules reside in the framework cavities. In the C222₁ structure at 20°C, H₂O and [C ₆H₁₆N]⁺ molecules filling the chiral channels along [001] are disordered, whereas, in the P2₁2₁2 ₁ structure at -127°C, they are perfectly ordered. The symmetry difference between structures at 20°C and -127°C is the result of a C222₁ → P2₁2₁2₁ second order phase transition that involves ordering of extra-framework protonated amine molecules and H₂O groups, and distortion of the flexible [(UO ₂)₆(MoO₄)₇(H₂O) ₂]^2- uranyl molybdate framework. On the basis of measurements of intensities of reflections that violate absence conditions of C-centering cell, the temperature of the phase transition is estimated as -11°C.