Sorry about bringing this again Tim, but I didn't want it to get lost. I had noticed that in the"Sion Switzerland" thread you mentioned the group of the "Rule of St. Augustine" being brought to Jerusalem prior to 1100, but Jacques de Vitry (who btw,did not reach the holy land himself until 1216), says the Canons Regulars were not even in "The Holy Sepulchre" until 1114 and ND of Mount Sion, much later. The Wiki article on ND of Mount Sion, says it was a small monastic order, which had abbeys on Mount Sion, on Mount Carmel, in southern Italy at Calabria and also in France.
No. These Canons Regular (under the Rule of St. Augustine) are said to have been brought from Europe by Godfrey de Bouillon and installed in the Church of the Holy Sepulchre in Jersualem. The confusion stems from the fact that this group of Canons Regular weren't chartered as their own distinct congregation (Congregation of Canons Regular of the Holy Sepulchre
) until 1114, leading some later chroniclers to conclude that they had no presence in the Church of the Holy Sepulchre or in Jerusalem prior to that time. The Congregation was given authority over the churches on Mount Zion, Mount Carmel, and the Mount of Olives.
There is a Papal bull dating from, I believe, 1143 which confirms the rights and possessions of the Canons Regular of the Holy Sepulchre, including possessions they were accorded by Godfrey de Bouillon himself, and as he died in 1100 this would put the Canons in Jerusalem by that time. They just weren't chartered as their own distinct congregation until 1114. There are also cartulary references from around the same time that refer to the abbots of N-D de Mont Sion as "priors", indicating that the abbey served as a priory (chapter house) to a larger congregation or order.
Also adding to the confusion is a completely separate and distinct "Equestrian Order of the Holy Sepulchre of Jerusalem", a chivalric rather than a religious order, that claims a very similar origin (brought by Godfrey to Jerusalem and housed in the Church of the Holy Sepulchre) though the documentary evidence it has cited in the past seems to refer to the Canons Regular rather than to armed knights.