I asked around in the good ol' C bty lines today and got this as my answer. As a quote from the 1RCHA site "The First Regiment of the Royal Canadian Horse Artillery is the senior unit of the regular component of the Canadian Forces. The Regiment traces its origin to 20 October 1871, when the first units of Canada's Permanent Force, A and B Batteries of Garrison Artillery, were authorized by Militia General Order No. 24. Stationed at Kingston and Quebec respectively, the batteries also functioned as Schools of Gunnery for Militia field batteries."
http://www.army.dnd.ca/1rcha/history.htm# Regimental%20History
So being the senior regiment being the first, the finest, we call have always call it "THE Regiment"
My 2 cents...