Building the Chancery quickly (particularly if Black Queen Catherine is in the game) can benefit any civilization. The building's efficacy can also be improved by the Cryptography and Police State policy cards, which will hamper enemy Spies from wreaking havoc across your lands. The downside of this building's Science-generation ability is that it is entirely reactive and dependent on other civilizations placing Spies in your cities.
A collection of consulates and embassies is termed a chancery. Here, diplomats gather to work out treaties and arrange deals… and (more likely than not) rub shoulders with spies. A chancery provides a centralized place to observe and monitor foreign agents within the country, to improve relations (and to try and figure out what other countries might be up to). It is larger and more exhaustive than a consulate.