Jersey fails with "IllegalStateException: No JAXB provider found for the following JAXB context" on JBoss EAp 6

Issue

 java.lang.IllegalStateException: No JAXB provider found for the following JAXB context: class com.sun.xml.bind.v2.runtime.JAXBContextImpl
        at com.sun.jersey.json.impl.JSONHelper.getJaxbProvider(JSONHelper.java:106)
        at com.sun.jersey.json.impl.DefaultJaxbXmlDocumentStructure.getXmlDocumentStructure(DefaultJaxbXmlDocumentStructure.java:76)
        at com.sun.jersey.json.impl.writer.Stax2JacksonWriter.<init>(Stax2JacksonWriter.java:169)
        at com.sun.jersey.json.impl.Stax2JsonFactory.createWriter(Stax2JsonFactory.java:105)
        at com.sun.jersey.json.impl.Stax2JsonFactory.createWriter(Stax2JsonFactory.java:85)
        at com.sun.jersey.json.impl.BaseJSONMarshaller.getXMLStreamWriter(BaseJSONMarshaller.java:111)
        at com.sun.jersey.json.impl.BaseJSONMarshaller.marshallToJSON(BaseJSONMarshaller.java:106)
        ...