© 2016. The American Astronomical Society. All rights reserved. We present a census of Lyα emission at z ≳ 7, utilizing deep near-infrared Hubble Space Telescope grism spectroscopy from the first six completed clusters of the Grism Lens-Amplified Survey from Space (GLASS). In 24/159 photometrically selected galaxies we detect emission lines consistent with Lyα in the GLASS spectra. Based on the distribution of signal-to-noise ratios and on simulations, we expect the completeness and the purity of the sample to be 40%-100% and 60%-90%, respectively. For the objects without detected emission lines we show that the observed (not corrected for lensing magnification) 1σ flux limits reach 5 × 10-18 erg s-1 cm-2 per position angle over the full wavelength range of GLASS (0.8-1.7 μm). Based on the conditional probability of Lyα emission measured from the ground at z ∼ 7, we would have expected 12-18 Lyα emitters. This is consistent with the number of detections, within the uncertainties, confirming the drop in Lyα emission with respect to z ∼ 6. Deeper follow-up spectroscopy, here exemplified by Keck spectroscopy, is necessary to improve our estimates of completeness and purity and to confirm individual candidates as true Lyα emitters. These candidates include a promising source at z = 8.1. The spatial extent of Lyα in a deep stack of the most convincing Lyα emitters with 'z' = 7.2 is consistent with that of the rest-frame UV continuum. Extended Lyα emission, if present, has a surface brightness below our detection limit, consistent with the properties of lower-redshift comparison samples. From the stack we estimate upper limits on rest-frame UV emission line ratios and find fC IV/fLyα ≳ 0.32 and fC III/fLyα ≳ 0.32, in good agreement with other values published in the literature.