The Hubble Frontier Fields program combines the capabilities of the Hubble Space Telescope (HST) with the gravitational lensing of massive galaxy clusters to probe the distant universe to an unprecedented depth. Here, we present the results of the first combined HST and Spitzer observations of the cluster A-2744. We combine the full near-infrared data with ancillary optical images to search for gravitationally lensed high-redshift (z greater than or similar to 6) galaxies. We report the detection of 15 I-814 dropout candidates at z similar to 6-7 and one Y-105 dropout at z similar to 8 in a total survey area of 1.43 arcmin(2) in the source plane. The predictions of our lens model also allow us to identify five multiply imaged systems lying at redshifts between z similar to 6 and z similar to 8. Thanks to constraints from the mass distribution in the cluster, we were able to estimate the effective survey volume corrected for completeness and magnification effects. This was in turn used to estimate the rest-frame ultraviolet luminosity function (LF) at z similar to 6-8. Our LF results are generally in agreement with the most recent blank field estimates, confirming the feasibility of surveys through lensing clusters. Although based on a shallower observations than what will be achieved in the final data set including the full Advanced Camera for Survey observations, the LF presented here goes down to M-UV similar to -18.5, corresponding to 0.2L(star) at z similar to 7 with one identified object at M-UV similar to -15 thanks to the highly magnified survey areas. This early study forecasts the power of using massive galaxy clusters as cosmic telescopes and its complementarity to blank fields.