The Grism Lens-Amplified Survey from Space (GLASS) is a Hubble Space Telescope (HST) Large Program, which will obtain 140 orbits of grism spectroscopy of the core and infall regions of 10 galaxy clusters, selected to be among the very best cosmic telescopes. Extensive HST imaging is available from many sources including the CLASH and Frontier Fields programs. We introduce the survey by analyzing spectra of faint multiply-imaged galaxies and z ≳ 6 galaxy candidates obtained from the first 7 orbits out of 14 targeting the core of the Frontier Fields cluster MACSJ0717.5+3745. Using the G102 and G141 grisms to cover the wavelength range 0.8-1.7 μm, we confirm four strongly lensed systems by detecting emission lines in each of the images. For the 9 z ≳ 6 galaxy candidates clear from contamination, we do not detect any emission lines down to a 7 orbit 1σ noise level of ∼5 × 10 -18 erg s-1 cm-2. Taking lensing magnification into account, our flux sensitivity reaches ∼0.2-5 × 10-18 erg s-1cm-2. These limits over an uninterrupted wavelength range rule out the possibility that the high-z galaxy candidates are instead strong line emitters at lower redshift. These results show that by means of careful modeling of the background - and with the assistance of lensing magnification - interesting flux limits can be reached for large numbers of objects, avoiding pre-selection and the wavelength restrictions inherent to ground-based multi-slit spectroscopy. These observations confirm the power of slitless HST spectroscopy even in fields as crowded as a cluster core.