A 'Chancery' is the type of building that houses a diplomatic mission

Diplomatic mission

A diplomatic mission is a group of people from one state or an international inter-governmental organisation present in another state to represent the sending state/organisation in the receiving state...

 or embassy. The building can house one or several different nations' missions.
The term Chancery has a rich history. Originally, there were two terms referring to the same structure, Chancery and Chancellory. The Chancery was the term used by the common people referring to a court of equity that they could access to resolve disputes. The aristocrats resolved their disputes either through the court of law or by bringing their problems to nobility directly.
Aristocrats often served on the court of equity and when they were in that position of power they referred to the structure as the Chancellory. The difference in terms was one of the many ways the upper class distinguished themselves from the lower class.
Even to this day the terms are still used independently. In the modern buildings the lower, or administrative positions, will still refer to the structure as the Chancery, while the higher level management will refer to the structure as the Chancellory.