The more proper term is curia, though people know what is meant by reference to chancellery or chancery.
Technically, the latter is the office of the chancellor. That role is found in canon 482.
§1. In every curia a chancellor is to be appointed whose principal task is, unless particular law determines otherwise, to see to it that the acts of the curia are gathered, arranged and safeguarded in the archive of the curia. §2. If it seems necessary the chancellor can be given an assistant, whose title is vice-chancellor. §3. The chancellor and vice-chancellor are automatically notaries and secretaries of the curia.
In practice, many diocesan bishops delegate additional authority to them today.
The diocesan curia consists of those institutions and persons which assist the bishop in the governance of the whole diocese, especially in guiding pastoral activity, in caring for the administration of the diocese, and in exercising judicial power (c. 469).