A train of attosecond pulses, synchronized to an infrared (IR) laser field, is used to create a series of electron wave packets (EWPs) that are below the ionization threshold in .helium. The ionization probability is found to strongly oscillate with the delay between the IR and attosecond fields twice per IR laser cycle. Calculations that reproduce the experimental results demonstrate that this ionization control results from interference between transiently bound EWPs created by different pulses in the train. In this way, we are able to observe, for the first time, attosecond wave-packet interference in a strongly driven atomic system.