The ternary iron chalcogenide, Fe(1.03)Se(0.57)Te(0.43) 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 approximately 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 approximately 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.