The structure of the Ni(111)(√3×√3)R30°-Pb surface phase formed by a nominal 1/3 monolayer of Pb has been investigated by medium-energy ion scattering using 100 keV H+ ions in three different incidence directions. The results show clearly that the Pb atoms occupy fcc hollow sites at the surface, but also favor a structure in which these are surrounded by Ni atoms to form a surface alloy phase. A surface alloy with a surface stacking fault, as has been found for the (√3×√3) surface alloy phases formed by Sb adsorption on Cu(111) and Ag(111), can be clearly excluded. The preference for a surface alloy structure is consistent with the results of an earlier low-energy ion scattering study, but we find significant differences in the quantitative structural parameters. This structural model also implies a considerable reduction of the effective radius of the Pb atoms relative to their size in bulk Pb, and this is discussed in the context of other quantitative structural studies of substitutional surface alloy phases