First-principles investigations of the thermodynamics of binary alloys using a cluster expansion have so far neglected the presence of vacancies. Here, we invoke a local cluster expansion as a perturbation to the standard binary cluster expansion to model the equilibrium vacancy concentration in a binary alloy as a function of temperature and alloy composition. We apply this approach to a first-principles investigation of the fcc Al 1−x Li x alloy ͑for x less than 0.3͒ which at x = 0.25 exhibits L1 2 superstructure ordering. The equilibrium vacancy concentration is predicted to be sensitive to the bulk alloy composition x in the ordered L1 2 phase, varying by more than an order of magnitude in a narrow interval of x at intermediate temperatures. Both in the solid solution and in the ordered L1 2 phase, the vacancy prefers a nearest neighbor shell rich in aluminum. In the L1 2 ordered phase, the vacancy predominantly occupies the lithium sublattice. The type of short-range order around a vacancy should affect the mobility of the constituents of the alloy and hence its interdiffusion coefficient.