Is use case narrative part of the UML?

Is use case narrative part of the UML?

A textual description of the business event and how the user will interact with the system to accomplish the task.

First of all, UML means Unified Modelling Language. It is a language which helps in designing and modelling software systems. So use case is not a part of UML. UML is a tool that helps to represent Use Cases (Among other things). And Use Case Modelling is an approach in requirement engineering for understanding and describing the functional requirements of a System.

It can be both narrative and graphical. Textual representation part is called use case specification while the graphical representation part is called Use case diagram.

So what is a use case?
A use case is a summary of scenarios for a single task or a goal like "pay bill" in the above image. And a Use case model typically consists of several use cases. It helps to provide a clear picture about the external actors (both users and external systems),the functional requirements of the system and the relationships among them which in turn leads to a better design.