High density components of an AlCoCrFeNi alloy, often described as a high-entropy alloy, were manufactured by binder jetting followed by sintering. Thermodynamic calculations using the CALPHAD approach show that the high-entropy alloy is only stable as a single phase in a narrow temperature range below the melting point. At all other temperatures, the alloy will form a mixture of phases, including a sigma phase, which can strongly influence the mechanical properties. The phase stabilities in built AlCoCrFeNi components were investigated by comparing the as-sintered samples with the post-sintering annealed samples at temperatures between 900 °C and 1300 °C. The as-sintered material shows a dominant B2/bcc structure with additional fcc phase in the grain boundaries and sigma phase precipitating in the grain interior. Annealing experiments between 1000 °C and 1100 °C inhibit the sigma phase and only a B2/bcc phase with a fcc phase is observed. Increasing the temperature further suppresses the fcc phase in favor for the B2/bcc phases. The mechanical properties are, as expected, dependent on the annealing temperature, with the higher annealing temperature giving an increase in yield strength from 1203 MPa to 1461 MPa and fracture strength from 1996 MPa to 2272 MPa. This can be explained by a hierarchical microstructure with nano-sized precipitates at higher annealing temperatures. The results enlighten the importance of microstructure control, which can be utilized in order to tune the mechanical properties of these alloys. Furthermore, an excellent oxidation resistance was observed with oxide layers with a thickness of less than 5 μm after 20 h annealing at 1200 °C, which would be of great importance for industrial applications.