EntityManager not useable in PostConstruct callback of StatelessSessionBean.

When trying to use the entity manager for a query in a PostConstruct callback in a StatelessSessionBean, execution fails with:

Caused by: java.lang.RuntimeException: EntityManager must be access within a transaction
at org.jboss.ejb3.entity.HibernateSessionFactory.getSession(HibernateSessionFactory.java:105)
at org.jboss.ejb3.entity.EntityManagerImpl.getSession(EntityManagerImpl.java:146)
at org.jboss.ejb3.entity.EntityManagerImpl.createQuery(EntityManagerImpl.java:39)
at some.package.postConstructCallback(SomeDAOBean.java:99)
... 26 more