Structural, magnetic, electrical transport, and heat capacity data are reported for single crystals of TlFe{sub 1.6}Se{sub 2}. This compound crystallizes in a tetragonal structure similar to the ThCr{sub 2}Si{sub 2} structure, but with vacancies in the Fe layer. The vacancies can be ordered or disordered depending on temperature and thermal history. If the vacancies are ordered, the basal plane lattice constant increases from a to {radical}5a. Antiferromagnetic order with the Fe spins along the c axis occurs below T{sub N} {approx} 430 K, as shown by single-crystal neutron diffraction, and the magnetic structure is reported. In addition, for the vacancy-ordered crystal, two other phase transitions are found at T{sub 1} {approx} 140 K and T{sub 2} {approx} 100 K. The phase transitions at T{sub 1} and T{sub 2} are evident in heat capacity, magnetic susceptibility, resistivity data, a and c lattice parameters, and the unusual temperature dependence of the magnetic order parameter determined from neutron scattering. The phase transitions at T{sub 1} and T{sub 2} result in significant changes in the magnetic moment per iron, with 1.72(6) {micro}B observed at 300 K, 2.07(9) {micro}B at 140 K, 1.90(9) {micro}B at 115 K, and 1.31(8) {micro}B for 5 K if themore » same 'block checkerboard' magnetic structure is used at all temperatures. The phase transitions appear to be driven by small changes in the c lattice constant, large magnetoelastic coupling, and the localization of carriers with decreasing temperature.« less