It is sort of possible but ill advised. This gets asked a lot in these forums so have a search for a more complete answer, but basically an entity in a relational database that does not have a unique identifier is not able to participate in relationships so is (by definition) not relational data. And you can't expect any tool whose job is to map between relational and OO data to work properly if you are mapping to soemthing that isn't relatioal.
There are workarounds (again, have a search of the forums) but none are perfect.
I had a client that insisted that primary keys really were not the necessary for oracle tables. Their tables had either no primary key, or a composite primary key referencing four or five tables.
Anyways, it was a complete nightmare. Really, in a relational database, a primary key is an extremely important concept. Hibernate really is fundamentally designed around primary keys and proper foreign keys. As Paul said, you can probably shoe-horn Hibernate into a non primary-key scenario, but I've never seen it done in a production environment, and it's certainly not a best practice.
Is there a situation you're in where you're being forced into tables without primary keys?