We report precise measurements of the structure factor S(k) as a function of the momentum transfer k for 4He at T=5.5 and 6.5 K in the density range 10<~ρ<~155 kg/m3. No theoretical predictions that can be tested against the data are available. The recent theoretical work by Bruch et al. at T=7.0 K, ρ=69.6 kg/m3 is in only limited agreement with our experimental data at T=7.0 K, ρ=69.0 kg/m3.