We show that high harmonic generation driven by an intense nearinfrared (IR) laser can be temporally controlled when an attosecond pulse train (APT) is used to ionize the generation medium, thereby replacing tunnel ionization as the first step in the well-known three-step model. New harmonics are formed when the ionization occurs at a well-defined time within the optical cycle of the IR field. The use of APT-created electron wave packets affords new avenues for the study and application of harmonic generation. In the present experiment, this makes it possible to study harmonic generation at IR intensities where tunnel ionization does not give a measurable signal.