We present 21-cm observations of a 10 × 2 deg2 region in the Virgo cluster, obtained as part of the Arecibo Galaxy Environment Survey. 289 sources are detected over the full redshift range (−2000 < vhel < +20 000 km s−1) with 95 belonging to the cluster (vhel < 3000 km s−1). We combine our observations with data from the optically selected Virgo Cluster Catalogue (VCC) and the Sloan Digital Sky Survey. Most of our detections can be clearly associated with a unique optical counterpart, and 30 per cent of the cluster detections are new objects fainter than the VCC optical completeness limit. Seven detections may have no optical counterpart and we discuss the possible origins of these objects. Seven detections appear associated with early-type galaxies. We perform H i stacking on the H i-undetected galaxies listed in the VCC in this region and show that they must have significantly less gas than those actually detected in H i. Galaxies undetected in H i in the cluster appear to be really devoid of gas, in contrast to a sample of field galaxies from the Arecibo Legacy Fast ALFA (ALFALFA).