The charge form factor of 4He has been extracted in the range 29 fm(-2) ≤ Q2 ≤ 77 fm(-2) from elastic electron scattering, detecting 4He recoil nuclei and electrons in coincidence with the high resolution spectrometers of the Hall A Facility of Jefferson Lab. The measurements have uncovered a second diffraction minimum for the form factor, which was predicted in the Q2 range of this experiment. The data are in qualitative agreement with theoretical calculations based on realistic interactions and accurate methods to solve the few-body problem.