We propose and use surface acoustic waves to control single-electron tunneling through an array of small tunnel junctions. The first experiments show that the wave traveling on the GaAs substrate couples to the islands of the array by modulating the potentials of their gates. We see cusps in the slope of the I-V curve at f=290 MHz around I=±ef. At 48 MHz and zero voltage biased to the ends we observe modulation of current by 3 pA around zero as a function of equal potential on the islands. Advantages of our method and problems, in particular the offset charge on GaAs, are discussed.