The iron chalcogenide FeSe has the simplest crystal structure among all the Fe-based superconductors. Unlike iron pnictides, FeSe exhibits no long- range magnetic order accompanying the tetragonal-to-orthorhombic structural distortion, which raises the fundamental question about the role of magnetism and associated spin fluctuations in mediating both nematicity and superconductivity. Here, using the chemical pressure, induced by substitution of Se by the bigger but isovalent ion Te, we study the complete system FeSe_1−xTe_x (0 ≤ x ≤ 1) using high-resolution thermal-expansion, specific-heat and resistivity measurements on high-quality single crystals. For low Te contents, superconductivity enhances nematicity below T_c in contrast to the behaviour at the optimal T_c at x = 0.5, where the behaviour is similar to that of iron pnictides. This highlights the existence of two different superconducting domes in the FeSe_1−xTe_x system.