Heteroepitaxial growth of Pb on the Ge(001) surface has been studied by He atom scattering. For low substrate temperatures, Pb is found to grow layer by layer with (111) orientation. A detailed analysis of the specular peak profile as a function of the He wave vector reveals that the step height of the growing monatomic terraces oscillates with the him thickness. This variation, initially as large as +/-15% around the value of the Pb(Ill) bulk interlayer spacing, gradually dampens out after the deposition of a dozen monolayers. This is direct evidence of quantum size effects affecting the interlayer distance of a growing metal film.