The ternary iron chalcogenide, Fe1.03Se0.57Te0.43 is a member of the recently discovered family of Fe-based superconductors with an ambient pressure T-c of 13.9 K and a simple. structure comprising layers of edge-sharing distorted Fe(Se/Te)(4) tetrahedra separated by a van der Waals gap. Here we study the relationship between its structural and electronic responses to the application of pressure. T-c depends sensitively on applied pressure attaining a broad maximum of 23.3 K at similar to 3 GPa. Further compression to 12 GPa leads to a metallic but nonsuperconducting ground state. High-resolution synchrotron X-ray diffraction shows that the superconducting phase is metrically orthorhombic at ambient pressure but pressurization to similar to 3 GPa leads to a structural transformation to a more distorted structure with monoclinic symmetry. The exact coincidence of the crystal symmetry crossover pressure with that at which T-c is maximum reveals an intimate link between crystal and electronic structures of the iron chalcogenide superconductors.