This paper does not discuss the authenticity or antiquity of the Holy Shroud. It addresses the problem of its historical appearance in the 1350s and its antecedents, if any, before that date. It is suggested that the object owed its creation (if a replica) or its transmission into Europe (if genuinely a relic) to the efforts of members of the Franciscan order. It speculates particularly on the role of Spirituals of that order aligned with Fra Angelo Clareno and his associates. The conclusions do not assert but suggest the thesis, and advance it as a line of inquiry meriting further pursuit.