- The Frontier Fields program is obtaining deep Hubble and Spitzer Space Telescope images of new "blank" fields and nearby fields gravitationally lensed by massive galaxy clusters. The Hubble images of the lensed fields are revealing nJy sources (AB mag > 31), the faintest galaxies yet observed. In this paper, we present high-redshift (z > 6) number count predictions for the full program and candidates in three of the first Hubble Frontier Fields images. The full program will transform our understanding of galaxy evolution in the first 600 million years (z > 9). Where previous programs yielded perhaps a dozen z > 9 candidates, the Frontier Fields may yield ~70 (~6 per field). We base this estimate on an extrapolation of luminosity functions observed between 4 < z < 8 and gravitational lensing models submitted by the community. However, in the first two deep infrared Hubble images obtained to date, we find z ~ 8 candidates but no strong candidates at z > 9. This might suggest a deficit of faint z > 9 galaxies as also reported in the Ultra Deep Field (even while excesses of brighter z > 9 galaxies were reported in shallower fields). At these redshifts, cosmic variance (field-to-field variation) is expected to be significant (greater than +/-50%) and include clustering of early galaxies formed in overdensities. The full Frontier Fields program will significantly mitigate this uncertainty by observing six independent sightlines each with a lensing cluster and nearby blank field.