[en] The deposition of 1/3 Pb monolayer at room temperature onto Ag(111) leads to a (√(3)x√(3))R30 deg. superstructure. We present here a detailed structural study of this surface structure by synchrotron radiation surface x ray diffraction (SR-SXRD) and scanning tunnel microscopy (STM). We show that Pb atoms are embedded into the silver top surface layer forming an ordered Ag₂Pb surface alloy despite the strong tendency of the system to phase separate in the bulk. Quenched molecular dynamics simulations allow us to interpret this ordering reversal, in terms of size-mismatch induced surface alloying