Transient growth properties are computed for a two-phase temporal mixing layer of immiscible fluids with interfacial tension. Large transient growth factors are found to occur at short times in parameter regimes characteristic of the primary breakup of a liquid. Optimal growth factors scale with the square of the Reynolds number, as for single-phase flow. The flow fields of optimal disturbances show liquid upflows and high-speed streamwise gas jets occurring together near the interface, suggesting transient growth as a possible mechanism for the formation of interfacial patterns. Optimal growth occurs for streamwise uniform disturbances with a spanwise wavelength proportional to the thickness of the gas boundary layer. For a coaxial jet, the predicted number of ligaments would be inversely proportional to the gas boundary layer thickness.