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The Bay Company Store. The Bay Is A Chain Of 91 Department Stores That Operate Across Parts Of Canada. It Is The Main Brand Of Hudson's Bay Company (Hbc), North America's Oldest Company.it Has Its Headquarters In The Simpson Tower In Toronto.in French, The Chain Is Known As La Baie, Short For Compagnie De La Baie D'hudson. The Chain Uses Both The English And French Versions Of The Name In Some Parts Of The Country.