In the present work, ternary Special Quasirandom Structures (SQSs) for a fcc solid solution phase are generated at different compositions, $x_A=x_B=x_C=tfrac{1}{3}$ and $x_A=tfrac{1}{2}$, $x_B=x_C=tfrac{1}{4}$, whose correlation functions are satisfactorily close to those of a random fcc solution. The generated SQSs are used to calculate the mixing enthalpy of the fcc phase in the Ca-Sr-Yb system. It is observed that first-principles calculations of all the binary and ternary SQSs in the Ca-Sr-Yb system exhibit very small local relaxation. It is concluded that the fcc ternary SQSs can provide valuable information about the mixing behavior of the fcc ternary solid solution phase. The SQSs presented in this work can be widely used to study the behavior of ternary fcc solid solutions.