According to the Abbey's website, the Old Church was begun in 63 CE at the same time that Joseph of Arimathea "possibly" founded a Christian community at Glastonbury. Monks were living there in 712 when King Ine of Wessex built the first stone church on the site. In 1184, a number of Abbey buildings were destroyed by fire. The Lady Chapel is believed to stand over the site of the Old Church.
More details about the Abbey are available at http://www.glastonburyabbey.com/.