No Hibernate Session bound to thread, and configuration does not allow creation of non-transactional one here

I have a legacy webapp which uses a servlet filter to wrap each request as follows

           
HibernateUtil.beginTransaction();
chain.doFilter(request, response);         
(boilerplate code which then calls one of the following...)          
HibernateUtil.commitTransaction();            
or            
HibernateUtil.rollbackTransaction();

HibernateUtil created a sessionFactory according to info in hibernate.cfg.xml as follows (I was using hibernate3 contextual sessions)

<session-factory>
<property name="connection.datasource">java:comp/env/jdbc/filmSource</property>
<property name="show_sql">true</property>
<property name="dialect">org.hibernate.dialect.MySQLDialect</property>      
<property name="hibernate.cache.provider_class">org.hibernate.cache.EhCacheProvider</property>
<property name="hibernate.current_session_context_class">thread</property>
<mapping resource="film/hibernate/Commission.hbm.xml" />
</session-factory>
</hibernate-configuration>

Everything worked fine.

However the app has now been integrated with Spring and I want to configure the Hibernate session in springs applicationContext.xml

Here is what I currently have in there..

  <bean id="myDataSource" class="org.springframework.jndi.JndiObjectFactoryBean">
    <property name="jndiName" value="java:comp/env/jdbc/filmSource"/>
  </bean>
  <bean id="mySessionFactory" class="org.springframework.orm.hibernate3.LocalSessionFactoryBean">
    <property name="dataSource" ref="myDataSource"/>
    <property name="mappingResources">
    <list>
      <value>film/hibernate/Commission.hbm.xml</value>
    </list>
    </property>
<property name="hibernateProperties">

<props>
  <prop key="hibernate.dialect">org.hibernate.dialect.MySQLDialect</prop>
  <prop key="hibernate.cache.provider_class">org.hibernate.cache.EhCacheProvider</prop>
  <prop key="hibernate.cache.use_second_level_cache">true</prop>
  <prop key="hibernate.current_session_context_class">thread</prop>
  <prop key="hibernate.transaction.factory_class">org.hibernate.transaction.JDBCTransactionFactory</prop>
  <prop key="hibernate.show_sql">true</prop>
</props>
    </property>
</bean>

<bean id="txManager" class="org.springframework.orm.hibernate3.HibernateTransactionManager">
<property name="sessionFactory" ref="mySessionFactory" />
</bean>

<bean id="hibernateUtil" class="film.web.framework.util.HibernateUtil"/>

and here is my hibernateUtil which has now been modified for Spring.

public class HibernateUtil {
      private static Log log = LogFactory.getLog(HibernateUtil.class);

      private static SessionFactory sessionFactory;

      @Autowired
      public void setMySessionFactory(SessionFactory value) {
            sessionFactory = value;      
      }
      

      public static SessionFactory getSessionFactory() {
            return sessionFactory;
      }

      public static Session getSession() {
            return getSessionFactory().getCurrentSession();
      }

      public static void beginTransaction() {
            getSessionFactory().getCurrentSession().beginTransaction();

      }

      public static void commitTransaction() {
            getSessionFactory().getCurrentSession().getTransaction().commit();
      }

      public static void rollbackTransaction() {
            getSessionFactory().getCurrentSession().getTransaction().rollback();
      }

}

The problem is when the request filter calls HibernateUtil.beginTransaction() I get the following error:

org.hibernate.HibernateException: No Hibernate Session bound to thread, and configuration does not allow creation of non-transactional one here.