Well… I say NO!
A user story can be a perfect short description of the use case, but it does not contain all the details you need for implementing, testing and maintaining the software.
A use case describes the what of the user story in much greater detail. And as a requirements engineer, when writing a use case description, you are forced to make it thoroughly logical – with no open ends.
So… user stories are great to uncover the who and the why, but you still very much need use cases to describe the what.
User stories are just another way to gather requirements. It is certainly a recommended technique if you are working in an agile environment. User stories are becoming more and more popular.