as in not administered by a priest

Troubles broke out in various parts of Bohemia, and drove many Romanist priests from their parishes. Almost from the first the Hussites divided into two sections, though many minor divisions also arose among them. Shortly before his death Hus had accepted a doctrine preached during his absence by his adherents at Prague, namely that of Utraquism, or the obligation of the faithful to receive communion in both kinds (sub utraque specie). This doctrine became the watchword of the moderate Hussites known as the Utraquists or Calixtines, from the Latin calix (the chalice), in Czech kališníci (from kalich); while the more extreme Hussites soon became known as the Orphans (sirotci) or Taborites (táborité), from the city of Tábor that became their centre.



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Note added at 9 hrs 50 mins (2005-07-26 07:33:31 GMT)
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\"Utraquists\" is correct in my point of view.

Jon Hus in his later years had written letters contending that \"laymen should be permitted to take the wine at the Communion\". For this doctrine the Utraquists now fought tooth and nail. They \"emblazoned the Cup on their banners\". They were the aristocrats of the movement; they were led by the University dons; they were political rather than religious in their aims; they regarded Hus as a patriot; and, on the whole, they did not care much for moral and spiritual reforms.

\"Sharing the communion chalice with the laity\" is absolutely not wrong, but I think there should be an English equivalent.

\"Utraquists - People (mostly aristocrats) who believed the communion chalice should be shared with the laity\"

The term is perfectly common in this theological/historical context. The background explanation provided by the other answerers are correct.

just enter "Hus lay chalice" and you'll get plenty of hits from good quality sources.