The dependence of the characteristic X-ray production on electron beam orientation is studied using very thin epitaxially grown single crystals. In crystals of Ag and Pd of thickness ~100 Å the L shell yield can change by more than a factor of 2 for small changes in orientation near the [111] direction. Theoretical analysis of the results shows that the different Bloch waves do not produce X-rays independently but that interference effects occur. The significance of these observations is discussed.