The long-range order parameter, S, of pure Cu₃Au and two Cu₃Au alloys containing 0.64 and 1.5 at. % Co was determined over the temperature range 325 to 387°C. In principle, the state of order in the ternary alloy (Cu₃Au)_1−XCo_X is described by two order parameters S₁ = Aα − Aβ, and S2 = Bβ − Bα where Aα is the fraction of α sites occupied by A atoms, etc. It is shown that S₂ − S₁ = Cα − Cβ = 0 as long as the Co atoms are randomly distributed on α and β sites. The values of S were measured at temperature using Warren's method [Warren, B. E. (1969). X-Ray Diffraction. Reading, Mass.: Addison-Wesley] applied to powder samples, employing the {110}, {210}, {211}, and {221, 300} superstructure and the {111}, {200}, {220}, {311}, and {222} fundamental reflections. The results on pure Cu₃Au are in relatively good agreement with earlier measurements, but in poor agreement with theoretical predictions, especially at temperatures above 360°C. Within the accuracy of the measurements, it is observed that cobalt, which is in solid solution in both alloys, has no effect on the experimentally determined values of S. The root-mean-square vibration amplitudes, 〈u²〉^1/2, of the Cu and Au atoms at 640°K were also estimated from the data, and it appeared that 〈u²〉^1/2_Cu decreased slightly with increasing Co content while 〈u²〉^1/2_Au increased.